Question

The curve y = ax2 + bx + c passes through the point (2, 32) and is tangent to the line y = 4x
at the origin. Find a, b, and c.

Answer 1

4a + 2b + c = 32

2ax + b = 4

b = 4

c = 0

a = 6

Answer 2

yes thats the right answer but i dont know how to get it....

Answer 3

Let's go step by step:

4a + 2b + c = 32 (The parabola passes through (2,32), so sub x=2, y=32)

Differentiating the original equation w.r.t. x to get 2ax+b,
equate the slope to the slope of the tangent line y=4x, slope =4, these give
2ax + b = 4, but at (0,0), x=0, so b=4

Since the curve passes through origin, c=0, in ax^2+bx+c=0

Substitute c=0, b=4 into 4a+2b+c=32 to get a=6 =>

b = 4 c = 0 a = 6

Answer 4

thanks so much

Answer 5

You're welcome!