Question

Find a parabola with equation
y = ax^2 + bx + c that has slope 6 at x = 1, slope −14 at x = −1, and passes through the point (2, 17).

Answer 1

dy/dx = 2ax + bx
when x = 1,
2a + b = 6

when x = -1
-2a +b = -14
add them
2b = -8
b= -4, then a = 5

to find c, sub in (2,17) into the original:
17 = 4a + 2b + c
17 = 20 -8 + c
c = 5

<b>y = 5x^2 - 4x + 5</b>

check:
for (2,17)
17 = 20 - 8 + 5 ---> true
dy/dx = 10x - 4
at x = 1, dy/dx = 10-4 = 6 , check!
at x = -1, dy/dx = -10 - 4 = -14 , check!

Answer 2

thanks. accurate, simple, and useful.

Answer 3

Direct, simple, clear - Thanks.

Answer 4

unclear that i had to do system of equations but i got it