Algebra and Trigonometry
Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Textbook Question
Chapter 5, Problem 1RE

For the following exercises, write the quadratic function in standard form. Then, give the vertex and axes intercepts.Finally, graph the function.

  1. f ( x ) = x 2 4 x 5

Expert Solution & Answer
Check Mark
To determine

Write the below quadratic function in standard form. Find the vertex and axes intercepts and graph the function

f(x)=x24x5

Answer to Problem 1RE

The standard form of quadratic equation isf(x)=(x2)29. Vertex is(2,9), while x-intercepts are(1,0)and(5,0)and y-intercept is(0,5)

Explanation of Solution

Given:

Quadratic functionf(x)=x24x5

Formula Used:

Let us consider a quadratic function in the form off(x)=ax2+bx+c, then the standard form of the equation is given as

f(x)=a(xh)2+k

Whereh=b2a

k=f(h)

Calculation:

Quadratic function is given as

f(x)=x24x5

Comparing the above function with general quadratic function, we get

a=1

b=4

c=5

Thus, the value ofhandkare calculated as follows:

h=(4)2×1

h=42

h=2

And,k=f(2)

k=(2)24(2)5

k=485

k=9

Now, the standard form of quadratic function is given as

f(x)=a(xh)2+k

Substituting the valuesa=1,h=2andk=9in above equation, we get

f(x)=1(x(2))2+(9)

f(x)=(x2)29

Thus, the standard form of quadratic equation isf(x)=(x2)29

Vertex is given as(h,k)

From above, the vertex is(2,9)

Now, we need to sketch the graph.

Algebra and Trigonometry, Chapter 5, Problem 1RE

From the graph,

x-intercepts are(1,0)and(5,0)

y-intercept is(0,5)

Conclusion:

Hence, the standard form of quadratic equation isf(x)=(x2)29. Vertex is(2,9), while x-intercepts are(1,0)and(5,0)and y-intercept is(0,5)

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Chapter 5 Solutions

Algebra and Trigonometry

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Find a third degree polynomial with real...Ch. 5.5 - Use Descartes’ Rule of Signs to determine the...Ch. 5.5 - A shipping container in the shape of a rectangular...Ch. 5.5 - Describe a use for the Remainder Theorem.Ch. 5.5 - Explain why the Rational Zero Theorem does...Ch. 5.5 - What is the difference between rational and...Ch. 5.5 - If Descartes’ Rule of Signs reveals a no changeof...Ch. 5.5 - If synthetic division reveals a zero, why should...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Remainder...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - For the following exercises, use the Factor...Ch. 5.5 - 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For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, use the Rational Zero...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - For the following exercises, find all complex...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - Use Descartes’ Rule to determine the possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, list all possible...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, use your calculator...Ch. 5.5 - For the following exercises, construct a...Ch. 5.5 - 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Find the domain of f(x)=4x5(x1)(x5).Ch. 5.6 - Find the vertical asymptotes and removable...Ch. 5.6 - Find the vertical and horizontal asymptotes of the...Ch. 5.6 - Given the reciprocal squared function that is...Ch. 5.6 - Given the function f(x)=(x+2)2(x2)2(x1)2(x3), use...Ch. 5.6 - What is the fundamental difference in the...Ch. 5.6 - What is the fundamental difference in the graphsof...Ch. 5.6 - If the graph of a rational function has a...Ch. 5.6 - Can a graph of a rational function have no...Ch. 5.6 - Can a graph of a rational function have...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain of...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the domain,...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, find the x- and...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, describe the local...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises, find the slant...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises. use the given...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, find the horizontal...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, write an equation for...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, use the graphs to...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, make tables to show...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, use a calculator to...Ch. 5.6 - For the following exercises, identify the removal...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, identify the...Ch. 5.6 - For the following exercises, express a rational...Ch. 5.6 - For the following exercises, express a rational...Ch. 5.6 - For the following exercises, use the given...Ch. 5.6 - For the following exercises, use the given...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.6 - For the following exercises, construct a rational...Ch. 5.7 - Show that f(x)=x+53 and f1(x)=3x5 are inverses.Ch. 5.7 - Find the inverse function of f(x)=x+43Ch. 5.7 - Find the inverse of the function f(x)=x2+1, on the...Ch. 5.7 - Restrict the domain and then find the inverse of...Ch. 5.7 - Find the inverse of the function f(x)=x+3x2.Ch. 5.7 - Explain why we cannot find inverse functions for...Ch. 5.7 - Why must we restrict the domain of a...Ch. 5.7 - When finding the inverse of a radical function,...Ch. 5.7 - The inverse of a quadratic function will always...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a graph to help...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, use a calculator to...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, find the inverse of...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.7 - For the following exercises, determine the...Ch. 5.8 - The quantity y varies directly with the square of...Ch. 5.8 - A quantity y varies inversely with the square of...Ch. 5.8 - A quantity x varies directly with the square of y...Ch. 5.8 - What is true of the appearance of graphs...Ch. 5.8 - If two variables vary inversely what will an...Ch. 5.8 - Is there a limit to the number of variables...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, write an equation...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use a calculator to...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use Kepler’s Law,...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5.8 - For the following exercises, use the given...Ch. 5 - For the following exercises, write the quadratic...Ch. 5 - For the following exercises, write the quadratic...Ch. 5 - For the following problems, find the equation of...Ch. 5 - For the following problems, find the equation of...Ch. 5 - For the following exercises, complete the task. 5....Ch. 5 - For the following exercises, complete the task. An...Ch. 5 - For the following exercises, determine if the...Ch. 5 - For the following exercises, determine if the...Ch. 5 - For the following exercises, determine if the...Ch. 5 - For the following exercises, determine end...Ch. 5 - For the following exercises, determine end...Ch. 5 - For the following exercises, determine end...Ch. 5 - For the following exercises, find all zeros of the...Ch. 5 - For the following exercises, find all zeros of the...Ch. 5 - For the following exercises, find all zeros of the...Ch. 5 - For the following exercises, based on the given...Ch. 5 - For the following exercises, based on the given...Ch. 5 - For the following exercises. based on the given...Ch. 5 - For the following exercises, use long division to...Ch. 5 - For the following exercises, use long division to...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use synthetic...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use the Rational Zero...Ch. 5 - For the following exercises, use Descartes’ Rule...Ch. 5 - For the following exercises, use Descartes’ Rule...Ch. 5 - For the following exercises. find the intercepts...Ch. 5 - For the following exercises. find the intercepts...Ch. 5 - For the following exercises, find the intercepts...Ch. 5 - For the following exercises. find the intercepts...Ch. 5 - For the following exercises, find the slant...Ch. 5 - For the following exercises, find the slant...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the inverse of...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, find the unknown...Ch. 5 - For the following exercises, solve the application...Ch. 5 - For the following exercises, solve the application...Ch. 5 - Give the degree and leading coefficient of the...Ch. 5 - Determine the and behavior of the polynomial...Ch. 5 - Determine the and behavior of the polynomial...Ch. 5 - Write the quadratic function in standard form....Ch. 5 - Given information about the graph of a quadratic...Ch. 5 - Solve the following application problem. A...Ch. 5 - Find all zeros of the following polynomial...Ch. 5 - Find all zeros of the following polynomial...Ch. 5 - Based on the graph, determine the zeros of the...Ch. 5 - Use long division to find the quotient. 2x3+3x4x+2Ch. 5 - Use synthetic division to find the quotient. If...Ch. 5 - Use synthetic division to find the quotient. If...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Use the Rational Zero Theorem to help you find the...Ch. 5 - Given the following information about a polynomial...Ch. 5 - Given the following information about a polynomial...Ch. 5 - Use Descartes’ Rule of Signs to determine the...Ch. 5 - For the following rational functions, find the...Ch. 5 - For the following rational functions, find the...Ch. 5 - Find the slant asymptote of the rational function....Ch. 5 - Find the inverse of the function. f(x)=x2+4Ch. 5 - Find the inverse of the function. f(x)=3x34Ch. 5 - Find the inverse of the function. f(x)=2x+33x1Ch. 5 - Find the unknown value. y varies inversely as the...Ch. 5 - Find the unknown value. 27. y varies jointly with...Ch. 5 - Solve the following application problem. The...
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