Find the quadratic function y=a(x-h)^2 whose graph passes through the given points. (10,-5) and (5,0)

Answer 1

The problem is to find a and h. The graph passes through (10. -5), so we can plug those numbers into the function:

-5 = a(10 - h)^2

The graph passes through (5, 0), so

0 = a(5 - h)^2

The key to finding a and h is the Zero Factor Theorem: If the product of two expressions is 0, at least one of the expressions must be 0. So, from the 2nd equation, either a is 0, or (5-h)^2 is. If a was 0, the function value y would _always_ be 0, so the graph couldn't pass through (10, -5) and the 1st equation couldn't be correct. Therefore (5-h)^2 is 0, which means h = 5. We can fill that in in the first equation:

-5 = a(10 - 5)^2

Solving that gives a = -1/5.

Therefore the quadratic function is y = -1/5(x - 5)^2.

Answer 2

y=a(x-h)^2.If the graph passes throgh the given points

(10,-5) and (5,0) then

-5=a(10-h)^2 and 0=a(5-h)^2 We have to solve the sistem

of equations with two veriables a and h.

So 0=a(5-h)^2 ⇔ a=0 or (5-h)^2=0 then h=5.We have

to substitute h=5 at -5=a(10-5)^2⇒-5=25a⇒a=-1/5.

The function is h(x)=-1/5(x-5)^2