The graph shows the height of a gold ball driven from a tee box as a function of the horizontal distance that it travelsequation in intercept formequation in vertex form will give brainliest

Intercept form  y=-5/64 (x) (x-160)

Vertex form  y =  -5/64 (x-80)^2 + 500

Step-by-step explanation:

The equation for a parabola in intercept form is y =a(x-p) (x-q)

where p and q are the intercepts.  We know that it intersects the x axis at 0 and 160, so we can substitute these in

y = a(x-0) (x-160)

y = a(x) (x-160)

We have to calculate the value of a.

Using the point (80, 500)

500 = a(80) (80-160)

500 = a (80) *(-80)

500 = a *-6400

Divide each side by -6400

a = -500/6400

a = -5/64

So the equation in intercept form is

y = -5/64 (x) (x-160)

The equation for a parabola in vertex  form is

y = a(x-h)^2 +k    

We know the vertex is (80,500)

y = a(x-80)^2 + 500

We need to pick a point to solve for a.  (0,0)

0 = a(0-80)^2 + 500

Subtract 500 from each side.

-500 = a(-80)^2

-500 = a (6400)

Divide by 6400

-500/6400 = a

-5/64 = a   ( Does this look familiar?)

y = -5/64 (x-80)^2 + 500

picture below