Please help!!!!!!!!!!!!!!!!!!!!!!!!!

Question

The graph of the function f(x) = x^2 - kx + k +8 touches the x-axis at one point, what are the possible values of k?

I don't really know how to do this, so please help!

Thanks a bunch!

Answer 1

f(x) = x² - kx + k + 8

For it to touch at only the x-axis at 1 point

The discriminate of the quadratic equation, b² - 4ac = 0

Compire the eqations ax² + bx + c = 0

substitute a = 1 , b = - k and c = k + 8 above the formula

(-k)² - 4(1)(k+8) = 0

k² - 4k - 32 = 0

k² - 8k + 4k - 32 = 0

Take out common factors.

k(k-8) + 4(k-8) = 0

(k - 8)(k + 4) = 0

k - 8 = 0  or  k + 4 = 0

k = -4, 8