f(x) = x^{2} − 4x

(b) Find its vertex and its x- and y-intercept(s). (If an answer does not exist, enter DNE.)

You will want to take this function from it's standard form to vertex form. This is of the form a(x-h)^2+k

To do this, you want to complete the square of x^2-4x by +4 and -4, so you get x^2-4x+4-4 = (x-2)^2 -4.

Therefore in vertex form, a=1, h=2, k = -4. The vertex is therefore (2, -4).

Now to solve the x-intercepts you set x^2-4x =0. You can factor to get x(x-4) = 0 and find x=0 or x=4.

So the smaller x-value intercept is (0,0) and the larger x-value intercept is (4,0)

The y-intercept just plugs in x=0 into x^2-4x, and you get (0,0).

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up