Question

Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

Answer 1

Answer:

f(x) = 2x(x-4)

f(x) = 2(x-2)^2-8

Step-by-step explanation:

Answer 2

The equation of the given Parabolic graph in the vertex form is $y = 2(x-2)^{2} -8$ and in the factor form is $y=2x(x-4)$.    

The values in boxes of Equation 1 are : 2, 4

The values in boxes of Equation 2 are : 2, 2, -8

The given graph is a Parabola.

The vertex of the parabola according to the graph is : (2,-8)

The graph's axis of symmetry is : $x = 2$

A general equation of a parabola with the vertex $(h,k)$ and the axis of symmetry equation $x = h$ is :

              $y = a(x-h)^{2}+k$

The points on the parabola from the graph are : (0,0), (2,-8), (4,0)

Here, we have $h = 2$ and $k=-8$. So, we get the equation of parabolas as follows :

            $y = a(x-2)^{2} -8$

Point (0,0) lies on the parabola and thus must satisfy the equation.

               $0 = a(0-2)^{2} - 8$

               $8 = 4a$

               $a = 2$

Thus, the equation of the given Parabola in vertex form is :

                $y = 2(x-2)^{2} -8$

Equation of parabola in factored form :

                 $y = 2(x-2)^{2} -8$

                $y = 2(x^{2} -4x+4)-8$

                $y = 2x^{2} -8x$

                $y=2x(x-4)$

Hence, the equation of Parabola in the vertex form is $y = 2(x-2)^{2} -8$ and in the factor form is $y=2x(x-4)$.        

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