f(x) = x2 − 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).
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