Answer:
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
