Vertex: Find b and c

Question

Find b and c so that y=−19x^2+bx+c has vertex (8,2).

Answer 1

The vertex form of the equation for a quadratic function

y = a(x – h)² + k

describes a parabola with the vertex point (h,k)

The equation given

y = –19x² + bx +c tells us the a = –19

and we're told that we want a quadratic function with the vertex point (8,2)

So to answer the question and find b and c we just plug

a = –19

h = 8

k = 2

into the vertex form equation y = a(x – h)² + k and algebraically convert the equation to its ax² + bx + c form.

y = a(x – h)² + k = –19(x – 8)² + 2 = –19(x² – 16x + 64) + 2 =

Just finish working out the last expression and

1. the coefficient in front of x will be your value for b
2. the constant term will be your value for c

Hope this helps. Just leave a comment if you have any questions.