Question

Write the Quadratic Formula

Answer 1

Answer:

$y=x^2-4$

Step-by-step explanation:

we know that

The function of the graph is a vertical parabola open upward

The vertex is a minimum

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

In this problem

Looking at the graph

The vertex is the point (0,-4)

substitute

$y=a(x-0)^2-4$

$y=ax^2-4$

To determine the value of "a" take a point in the graph

I take the point (3,5)

substitute the value of x and the value of y and solve for a

$5=a(3)^2-4\\9a=5+4\\9a=9\\a=1$

therefore

The equation of the quadratic function is

$y=x^2-4$