Question

What is the function for the graph below?

Answer 1

The equation of the quadratic function graphed is: y = -1/4 (x + 2)² + 3

How to write the equation

Quadratic equation in standard vertex form si

y = a(x - h)² + k

where a = 1/4p

The vertex

v (h, k) = (-2, 3)

h = -2

k = 3

The graph passed through (-4, 2) we use it to solve for a

2 = a(-4 - (-2))² + 3

2 - 3 = a(-4+ 2)²

-1 = a(-2)²

-1 = a * 4

a = -1/4

Plugging in the values we have the equation

y = -1/4 (x + 2)² + 3

Answer 2

The equation of the graphed function is f(x) = -(2x - 3)(2x +11)

How to determine the equation of the graphed function

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

Zeros: x = 1.5 and -5.5

The zeros have a multiplicity of 1 each

So, we have the expression in factored form to be

f(x) = -(x - 1.5)(x + 5.5)

This can be expressed as

f(x) = -(2x - 3)(2x +11)

Hence, the equation of the graphed function is f(x) = -(2x - 3)(2x +11)