Find the vertex of the quadratic function f(x) = x² – 6x + 42 then express the quadratic function in standard form f(x) = a(x – h)² + k and state whether the vertex is a minimum or maximum. Enter exact answers only, no approximations.

Q: 4. Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not…

A: 4. cubic equation must have at least 1 real solution so it must have cut the x-axis once since if…

Q: Find the domain and range of the quadratic function whose g 3) The maximum is -5 at x = -1

A: Explanation of the answer is as follows

Q: 9. Determine the equation of the quadratic function that has x-intercepts 1+ V3 and 1- V3 and passes…

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =…

A: We compare  f(x) = 3x2 - 12x + 1 with  f(x) = ax2 +bx + c  So, a=3, b=-12, c=1

Q: Find the coordinates of the vertex for the parabola defined by the quadratic function f(x) = -2(x +…

A: Given quadratic function f(x) = -2(x + 4)2 - 8     ...(1)

Q: What are the coordinates at the minimum point of f(x)= x2-4x+3?

A: f(x)= x2-4x+3 is a parabola with a positive lead coefficient so it will have a minimum at the…

Q: 40. Express the quadratic function f(x) = x2 - x - 6 in vertex form, and sketch its graph (showing…

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Q: Find a formula for the quadratic function whose graph has y-intercept at y=11 and zeros at x=1 and…

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Q: Find a formula for the quadratic function whose graph has its vertex at (5,2) and its y-intercept at…

A: Find a formula for the quadratic function whose graph has its vertex at (5,2) and its y-intercept at…

Q: Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output will be maximum?

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Q: Find the maximum and minimum values of 3x -2x³- 6x² + 6x +1 in the interval (0, 2).

A: Given that f(x)=3x4-2x3-6x2+6x+1  We have to find maximum or minimum value in (0,2)…

Q: Find the rule of the quadratic function f (x)= a(x-h)² +k whose grapn has a vertex at (-15, 18) and…

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Q: Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at…

A: SolutionA parabola has horizontal intercepts(roots) at x = 6.1 and x = 1.4and passes throught the…

Q: Find the maximum or minimum value of the quadratic function g(x) = 2x2 + 6x + 1. The ---Select---…

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Q: Find the coordinates of the vertex for the parabola defined by the quadratic function f(x) = -2x2 +…

A: The given quadratic function f(x) = -2x2 + 8x - 1   Known fact: The standard form of the quadratic…

Q: 4) Find the equation of a quadratic function with a maximum value at (2,5) and a vertical intercept…

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Q: Find the maximum/minimum value of y = 10-4x - 3x² and where it occurs using completing the square.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find the Critical points of the ff equation and Determine the Maximum and Minimum. - 1. y= 2x² - 12x…

A: A detailed solution is given below.

Q: The total daily profit (in thousands of pesos)of a certain food company for the sale of ... x boxes…

A:

Q: 4. Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not…

A: A cubic function is one in the form f(x)=ax3+bx2+cx+d. The "basic" cubic function, f(x)=x3 , is…

Q: 2.a. Find the maximum and minimum values of the function: y = 3x² 18x +31 -

A: We have to find the maximum and minimum values of the given function y=3x2-18x+31 .

Q: Find the value/s of x for which y=3x^4-4x^3+1 is maximum?

A: y=3x4-4x3+1 Differentiating with respect to x, we get dydx=34x3-43x2+0=12x3-12x2 Now to find…

Q: Express y=-2x2+6x+12 in completing the square form. Hence, find the maximum/minimum values of each…

A: We will find out the required values.

Q: Find the absolute maximum value of y = x³-3x2 + 2 in the interval [-1,3]. (-1,-2) (0,2) O (1,0)…

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Q: The total daily profit (in thousands of pesos)of a certain food company for the sale of ... x boxes…

A: Given:   Now, we need to find the value of x such that P(x) is the maximum. For simplicity, we plot…

Q: The extremum of f(x) = -5x2+4x+17 is a minimum.

A:

Q: Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more…

A: Consider the provided question, Yes, cubic function have at least one real root (x-intercept) but…

Q: Find the minimum or maximum value of the quadratic function. f(x) = −2x2 + 4x − 7  ---Select---…

A: To find the minimum or maximum value of the given quadratic function.

Q: To put the quadratic function f(x) = ax + bx + c in standard form, we complete the --Select- Select-…

A: To find: To put the quadratic equation in standard form, we complete the  ________________________

Q: Consider the function of y = 5x + 2x- 3x and find the maximum and minimum points.

A: Without wasting any time, differentiate the function w.r.t x on both the sides, dy/dx = 15x2 + 4x -…

Q: a firm hasn total weekly revenue in dollars for its product given by R(x)=2800x-8x2-x3, where x is…

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Q: Discuss the maximum and minimum of x2+y2+6x+12

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Q: 5. Sketch a possible graph of a quadratic function which has two real roots (one positive, one…

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Q: At which value does the function g(x)= 3x^4 - 4x^3 attain a minimum and what is the minimum value?.

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Q: f(x) = 2x3+az? 12z has alocal maximum at z -2,then a

A: f(x)=2x3+ax2-12x  has a local maximum at x=-2then we have to find the value of a

Q: Find the point on the graphf(x)=4-x^2 that is closest to the point (0,1)

A: To find the point on the graph f(x)=4-x2 that is closest to the point (0,1)

Q: 1. Pick a point where that is NOT on any of the lines: a = 0 y = 0 y = x y = -x 2. Find the equation…

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Q: Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not more…

A: Answer

Q: The annual total revenue for a product is given by R(x)=30,000x−6x2 ​dollars, where x is the number…

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Q: Find the standard form f(x) = a(x – h)² +k__of the quadratic function that has a vertex at and an X…

A: Given that: vertex =-12,-19 and x-intercept =-32,0. To find the standard form of the quadratic…

Q: A company has sales (measured in millions) of $50, $60, and $75 during three consecutive years. Find…

A: Given Sale in 1st year is $50 Sale in 2nd year is $60 Sale in 3rd year is $75 Let the quadratic…

Q: 4) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in…

A: Maximum number of mosquitoes

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function : f(x) =…

A: We have to find coordinates of the vertex for the parabola defined by quadratic function:…

Q: 3. Write the quadratic function whose maximum value is 5 when x = 2 and whose parabola passes…

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Q: use the result to derive the quadratic splines and estimate the value at x = 5.0

A: The data given is as follows: i xi fxi 1 3 2.5 2 4.5 1 3 7 2.5 4 9 0.5 Three quadratic…

Q: 11. Given the quadratic function f (x) = 2x2 – 12x + 14 Express the equation in standard form (also…

A: The standard form or vertex form of an equation is given by y=ax+h2+b, where x, y are variables and…

Q: Find a formula for the quadratic function whose y-intercept of y = 3 and x-intercepts at x = 1,…

A: Given: y-intercept y=3 x-intercept at x=1,4

Q: Express the quadratic function f(r) = x² - x - 6 in vertex form, and %3D sketch its graph (showing…

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Q: Find a formula for the quadratic function whose graph has vertex (1,−3) and y-intercept −7   f(x)=

A: We have given the vertex (1,−3) and y-intercept −7.