Suppose that for a function f (x), that it has exactly one zero, (or 1 x-intercept), which of the following must be true?   -f(x) is linear and has a positive slope -f(x) is quadratic  -the equation for f(x)=0 has a complex solution -there is exactly one point on the graph

Q: f(x) = −x2 + 6x − 12 y-intercept(x, y)=

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

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Q: Find the standard form f(x) = a(x – h)²+k__of the quadratic function that has zeros of 9. and and…

A: The standard form of the quadratic function is f(x)=a(x-h)2+k. This form has zeros at 15 and 95.…

Q: Find a quadratic function f whose graph matches the one below. f(x) =D (-2,3) (0,1) of

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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 the quadratic function f(x) = ax2 + bx + c for which f(-1) = 5, f(1) = 3, and f(2) = 5.

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Q: The range of the quadratic function f (z) is the set of real numbers less than or equal to 1. If the…

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Q: Suppose f (x) = x² + 2x + 1. Find the vertex, vertical intercept, and x-intercepts of this quadratic…

A: The objective of the question is evaluate vertex , vertical intercept and  x-intercept.

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: 2. The quadratic function y =9-x² +4x written in standard form would be (1) y=-x² +4x+9 (3) y=x²…

A: Answer (2) We have to write the quadratic function  y = 9 - x^2 + 4x in standard form

Q: The degree of f(x) is v and the leading coefficient is There are| distinct real zeros and relative…

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Q: A fast-food restaurant has a cost of production C (x) = 11x + 108 and a revenue function R(x) = 5x.…

A: when production cost become equal to revenue then that point will be equillibrium and if revenue…

Q: How does the linear factorization of f(x), that is, AX)=an (x-c1)(x-c2) (x-C). show that a…

A: Here the linear factorization of the function f(x) is given as:…

Q: Here is the graph of a quadratic function f. Select at least two equations that could define the…

A: Graphically roots are those x-coordinates where graph of function touches or cuts the x-axis. In the…

Q: Consider f(x)=ax3+bx2+cx+d Under what conditions on a,b,c,and d does the graph of a cubic function…

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Q: At what points of ℝ2 is a rational function of two variables continuous?

A: Given  The  ℝ2 is a rational function of two variables .

Q: Find an equation of the cubic polynomial f(x) = ax3 + bx2 + cx + d that passes through the given…

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Q: Find the first, second, and third derivatives of the func- tion. W (t) = 5t² + 4e*.

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative…

Q: What is the equation of a quadratic function y=f(x) with two irrational zeros, negative square root…

A: The equation of a quadratic function y=f(x) with two irrational zeros, negative square root of h and…

Q: 17. If f(x) =x -6x +14 and g(x) -x -20x -k, determine the value of k so that there is exactly one…

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Q: by graphing the standard quadratic function f(x)=x². Then use transformations of this graph to graph…

A: Please refer to the image below

Q: In Problem,explain why the facts given are contradictory.

A: Zero of a function is a point in its domain for which the function takes the value equal to 0. A…

Q: Show that if the quadratic polynomial f (x) = x2 + rx + s takes on both positive and negative…

A: Find the real roots of the polynomial,

Q: Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation:…

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Q: (4) Suppose the coefficients of the cubic polynomial p(x) = a + bx + cx² + dx³ satisfy the equation…

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Q: the graph of the quadratic function f(x) = x2 + dx + 5d has its vertex on the x-axis, what are the…

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Q: 1. Express the quadratic function f1x2  x2  x  6 in standard form, and sketch its graph.

A: Given: f(x)=x2−x−6

Q: A fast-food restaurant has a cost of production C (x) = 13x + 126 and a revenue function R(x) = 6x.…

A: Given: C(x)=13x+126 R(x)=6x The company will start to turn a profit when the revenue function will…

Q: What is the equation of a quadratic function y = f(x) with two irrational zeros,-h and h where h is…

A: Given,         The equation of a quadratic function y=fx with two irrational zeros, -h          and…

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: 17. If f(x) = x-6x +14 and g(x)-x -20x -k, determine the value of k so that there is exactly one…

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Q: If f'(x) has no roots, then f (x) has exactly one root. If f (x) has three roots, then f'(x) has at…

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Q: Is f(x) =x−3/x + 1 a rational equation? Prove the answer with a solution if possible.

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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: Find the standard formf (x) = a(x – h)² + k of the quadratic function that has a vertex at (-2, 5)…

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Q: 18. What quadratic function that passes the point (2, 1) and to its only zero of 3? A. y = x2-6x - 9…

A: Follow the procedure given below.

Q: Given the quadratic function shown below whose turning point is (2, – 4), which of the following…

A: Here we use the graph to tell about the interval of decrease. If the slope of the tangent line…

Q: Find the zeros of the quadratic function: f (x) = x² + 10x + 24 %3D x = 8 Cx = 3 X = 4 X = 6 X = -8…

A: see below the answer

Q: Identify the quadratic function from the graph -2 -4 -3 -2 -1 2 4 a) f(x) = x² – 4x + 5 b) f(x) = x²…

A: Consider the quadratic equation given in part (a), fx=x2-4x+5 from the graph, it can be observed…

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: Find the quadratic polynomial whose graph goes through the points (-1, 3), (0, 1), and (1,7). f(x) =

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Q: The polynomial of degree 33, P(x)P(x), has a root of multiplicity 22 at x=3x=3 and a root of…

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Q: Find the quadratic function f(x) = ax2 + bx + c for which f(-2) = -4, f(1) = 2, and f(2) = 0.

A: fx=ax2+bx+c,  f-2=-4,  f1=2  and f2=0. Now put f-2=-4 in fx=ax2+bx+c, we get…

Q: 17. If f(x) = x -6x +14 and g(x)- x -20x -k, determine the value of k so that there is exactly one…

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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: Given the function g(x) – 5(x – 7)*(x + 1)°(x – 4), its roots are and their multipicities are

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Q: Use the vertex  (h, k)  and a point on the graph  (x, y)  to find the general form of the equation…

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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: 1. Determine the equation in standard form of the quadratic function shown. 在 (-2,0) (3.0) (4, -3)…

A: Equation of the quadratic equation.

Q: Sketch the graph of the quadratic function. f(x) = x² + x - 4 y -10 -5 -10 40 20 -20 -40 5 10 y 40…

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.