Question

The curve y = ax2 + bx has gradient 8 when x=2 and has gradient -10 when x=-1. Find the value of a and the value of b.​

Answer 1

Step-by-step explanation:

you know that f'(2) = 0

2ax+b = 0 at (2,8)

4a+b = 0

4a+2b = 8

So, b=8

a = -2

y = -2x^2 + 8x

or, without calculus, you know that

-b/2a = 2 since the vertex is there.

so b = -4a

y(2) = 8, so

4a + (-4a)(2) = 8

a = -2

so b = 8