With what integer a is the the graph y=4x-2 the tangent line of y=ax^2+28x+14?

1 Answer
Dec 17, 2017

a = 9

Explanation:

The given equations will have the same y value at point of tangency, therefore, we may set the right sides of both equation equal:

4x-2= ax^2+28x+14

0 = ax^2+24x+16" [1]"

The slope of the tangent is 4, therefore, we must set the first derivative of the quadratic equal to 4:

dy/dx = 2ax+28

4 = 2ax+28

-24=2ax

x = -12/a" [2]"

The substitute equation [2] into equation [1]:

0 = a(-12/a)^2+24(-12/a)+16

0 = 144/a-288/a+16

0 = 144-288+16a

16a = 144

a = 9