Determine the quadratic function of the form f(x) = a(x-h) +k whose graph is given on the right. 40- f(x) =D %3! (4,1) -10 10 (3,0) 10

Q: Find the quadratic function f(x) = ax + bx+c for which f(1) = -9, f(-3) = 51, and f(3) = 9. What is…

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Q: Find the equation of the quadratic function f whose graph is shown below. 14 12- 10- s(x) = 0 | (7,…

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Q: 2) Find the formula for a quadratic function that passes through the points (4, 3) and (2, o a as…

A: To Find :- The formula for a quadratic function that passes through the points (4, 3) and (2, 8) and…

Q: 2 -2 2 -2 6,

A: Quadratic graph

Q: The Range of the quadratic function f(x) = -x² + 18x + 52 is O [-9, 00) O [52, 0) O (0,9] O (-∞0,…

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Q: Find the equation of the quadratic function g whose graph is shown below. g (x) = 0 -12 -10 -2-…

A: We have given graph of the function  Let equation of the quadratic function  gx=ax-h2+k…

Q: Select the graph of the related function. Then use the graph to solve the quadraticequation. 40 40…

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Q: Use a graphing utility to graph the quadratic function f(x) = −2x2 + 10x. Find the x-intercept(s) of…

A: x-intercept: The point at which the graph intersects the x-axis is called x-intercept.  Any…

Q: Find the equation of the quadratic function g whose graph is shown below. e (x) = 0 6- -12 -10 (-5,…

A: The given points are, (-5,-2) and (-4,-4)

Q: Determine the x-intercept(s) of the quadratic function f(x)=x²+ 2x+ 2. no x-intercept(s) (-7, 0),…

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Q: 3 . Write the quadratic function C(x) - x -x- 57 in vertex f c(x) c(x) = (x- 1) - 6 リ4 c(x) - c(x) -…

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Q: The graph of a quadratic function f(x) is shown above. It has a vertex at (2, 1) and passes the…

A: The graph of a quadratic function fx has vertex 2,1 and passes through the point 0,-1. Standard…

Q: Please help me solve this question

A: Consider the quadratic equation

Q: What is the quadratic function that corresponds to this graph? Use feet as a standard of measure and…

A: A graph, with vertex (0,3) and x intercept (0.44,0)

Q: 5. Find the x-and y-intercepts of the graph of the quadratic function. f(x) =x2 + 2x + 1…

A: Given fx=x2+2x+1

Q: Find the quadratic function y=ax2+bx+c whose graph passes through the given points ​(−1​,−16​),…

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Q: The graph of the quadratic function f(x) = (x - m)(x - n) is given below. If the x-coordinate of the…

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Q: Graph the quadratic function f(x)=−4x 2−40x−84. Give the​ (a) vertex,​ (b) axis,​ (c) domain, and​…

A: f(x)=-4x2-40x-84       =-4(x2+10x+25-4)       =-4(x+5)2+16                   ...(1) Compare equation…

Q: Determine the quadratic function f(x)= ax+bx + c, whose graph is given. 10 5+ +++> 10 X -10 -5 F0,…

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Q: 18. Find the quadratic function from the table of values below. -5 -4 -3 -2 -1 -6 -1 2 3 -1 -6 a) y…

A: 19) Given : T=4h when h is doubled, h'=2h so T'= 4(2h)  T'=2(4h)= 2T  so when h is doubled T also…

Q: The quadratic function f(x) = 2? + bæ + 49 is a perfect square trinomial. What is a possible value…

A: A perfect square trinomial  will have a discriminant b2-4ac=0.

Q: 7) Write the quadratic function, f(x)=x²-2x-8 in vertex form and then find all of the following: a.…

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Q: 7) Write the quadratic function, f(x)=x²-2x-8 in vertex form and then find all of the following: a.…

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Q: Find the equation of the quadratic function f whose graph is shown below. -2 10 12 7 (3, – 2) -2-…

A: Given, Graph of quadratic function is passing through the points 3, -2  and 5, -10  We have to find…

Q: Given (-1,12) is the maximum point for a quadratic function f(x) = 4h-(2k+x)²,where h and k are…

A: Given quadratic function is fx=4h-2k+x2

Q: Using quadratic interpolation, find the maximum of the function f (x)= 13cosx-(x13/10) with the…

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Q: Find the equation of the quadratic function g whose graph is shown below. -10 -8 (-2, – 5) . 8 (x) =…

A: The general equation of downward opening parabola is  (x-h)2=4p(y-k), where (h,k) is the vertex.…

Q: The Range of the quadratic function f(x) =-² +24r + 55 is O (-55, 12] O (-00, 55] O [55, 00) О (),…

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Q: Questlon Enter a quadratic function after changlng from vertex form, y = a(x-h)+k, to standard form,…

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Q: Graph the quadratic function f(x) = (x + 4)². Give the (a) vertex, (b) axis, (c) domain, and (d)…

A: Given equation of parabola,, f(x)=(x+4)2

Q: If a quadratic function has the rule f(x) = (x – h)² + k, what will cause a horizontal translation?…

A: Given query is to find the correct answer for the horizontal translation.

Q: Which quadratic function matches this graph? O f(x) = x² − 14x +45 O f(x)=x²- 11x + 28 O f(x) = x² +…

A: As per our guidelines we have to answer the first question if multiple questions are posted at a…

Q: Consider the Quadratic function f(x) = 4x-49. Its vertex is ( The x value of its largest x-intercept…

A: Quadratic or parabola function in vertex form: (y-k) = a(x-h2) y = a(x-h2) + k  where (h, k) =…

Q: Find the vertex of the graph of the quadratic function. f (x) = -x² + 12r – 36 O (0, 6) O (-6,0) O…

A: Given quadratic function

Q: 6. [A] a)Write the family of a quadratic function with zeros of (-1, 0) and ( 5, 0). b) Determine…

A: Quadratic function is a polynomial of degree 2 in one variable .It is of the form y=ax2+bx+c where…

Q: Find the quadratic function y = ax + bx +c whose graph passes through the given points. (1, – 1), (–…

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Q: Determine the x-intercept(s) of the quadratic function f(x)=x²+ 8x+ 12. (-6, 0), (–5, 0) no…

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Q: Which quadratic function has the largest maximum? (1) h(x)= (3- x)(2+x) (3) k(x) =-5x² -12.x +4 (2)…

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Q: If a quadratic function has the rule f (x) = (x – h)² + k, what will cause a vertical translation?…

A: The answer is given below.

Q: Q5. Use the graph of the quadratic function shown below: to identify its equation: Hint: It has a…

A: We need to identify the given curve equation.

Q: Write the quadratic function in the form f(x) = a (x-h)²+k. Then, give the vertex of its graph. 2 f…

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Q: Write the quadratic function in the form f(x) = a (x-h)-+k. Then, give the vertex of its graph. f(x)…

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Q: 4. Consider the graph of a quadratic function. 10 -10 -9 -8 -7 8 9 10 -3 -5 -6 -7 8- -9 10 Which…

A: topic -quadratic functions

Q: Write the equation of a quadratic function with roots at -4 and -2, and a vertex at (-3, 1). Write…

A: The quadratic equation with roots at -4 and -2 is given by: y=C(x+2)(x+4) where C is the constant.

Q: Find two quadratic functions, one that opens upward and one that opens downward, whose graphs have…

A: A quadratic function with x-intercepts (-4,0),(5,0) then gives (x+4) and (x-5) are factors of…

Q: What is the equation of the quadratic function g(x)? * -4 -3 -2 -1 1 2 3 4 g(x) -9- -16 -21 -24 -25…

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Q: How do you find the largest open interval of the domain over which function is increasing? With the…

A: This parabola is facing downwards because the leading coefficient is = -1/2 which is negative.  So…

Q: C. Transform the Standard Quadratic function to vertex form.Show your solution 1. )= 4x² +8x – 6 2.…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.