Determine the equation of the quadratic function from its gr

Determine the equation of the quadratic function from its graph.

y =

Solution

We will use the vertex form: y = a(x - h)² + k.

We know the vertex is (-1.5,10) = (h,k), so h =3 - (3-(-6))/2 = -1.5 and k = 10.

If we substitute, we get y = a(x + 1.5)² + 10.

Another random point on the graph is (3,0)

substitute the point in equation

0 = 20.25a+10

a = -10/20.25 = -2/4.05

The quadratic equation is

y = (-2/4.05)(x + 1.5)² + 10.

y = (-2/4.05)(x^2+3x+2.25)+10