Question

Find b and c so that y = -20x^2+bx+c has vertex (-10, 3)

Answer 1

The vertex form of a parabola is \(y = a(x - h)^2 + k\)

We are given that (h,k) = (-10,3) and a = -20 so

\(y = -20(x + 10)^2 + 3\) which expands to:

\[y = -20(x + 10)(x + 10) + 3
\\= -20(x^2 + 20x + 100) + 3
\\ = -20x^2 - 400x - 2000 + 3
\\ = -20x^2 - 400x - 1997\]

Therefore b = -400 and c = -1997

To check:
http://www.wolframalpha.com/input/?i=-20x%5E2+-+400x+-1997+%3D+-20%28x+%2B+10%29%5E2+%2B3

Answer 2

Thanks. That helped me greatly to understand the solution.

Answer 3

I just checked and the answers that I got were b = -400 and c = -2003... my steps:

Answer 4

-b / 2a = -b / 2(-20) = -b / -40 = - 10(-40)
-b = 400
b = 400

-3 = -20(-10)^2+-400*-10+c
-3 = -2000 + 4000 + c
-3 = 2000 + c
c = -2003

Answer 5

@Hero

Answer 6

If you have doubts check with wolframalpha