SOLUTION: The parabola has a turning point at (z, -8). It intersects the y-axis at y=10 and one of the x-intercepts is x=5. Find: the value of z

Question 1037252: The parabola has a turning point at (z, -8). It intersects the y-axis at y=10 and one of the x-intercepts is x=5. Find:
the value of z
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let the quadratic function be , where x=5 is one of the roots (as given via the x-intercept), and x = r is the other root.
Since y = 10 is the value of the y-intercept, the constant term in the quadratic function must be equal to 5ar, and moreover, 5ar = 10, by hypothesis.
==> ar = 2.
Since the turning point (or the vertex of the parabola) is always midway between the two roots, it follows that .
==> , or
.
Divide this equation by the equation ar = 2, giving
, or,
or
, after expanding and simplifying.
==> r = 25 or r = 1.
If r = 25, then a = 2/25.
If r = 1, then a = 2.
Hence there are two possible answers:
(i) The function has , while,
(ii) The function has .
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