The parabola has the turning point at (z, -8) and y-intercept at 10, and an x-intercept at x=5.
What is --- value of z?
The equation of parabola?
The equation can be written in turning point form as .
Substitute the known points (0, 10) and (5, 0) to get two equations in the unknowns a and z. Solve these two equations simultaneously to get the values of a and z.
Another approach . . .
The parabola has the turning point at ,
and y-intercept at , and an x-intercept at
Find and the equation of the parabola.
The general equation of a parabola is: .
We are given three points on the parabola.
We are told that: .
We have: .
And we have: .
Substitute into : .
Substitute  and  into : .
. . and we have: .
There are two solutions . . .