A quadratic function is given.

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f(x) = x2 − 4x

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

vertex    (xy) =
x-intercepts    (xy) =
 (smaller x-value)
(xy) =
 (larger x-value)
y-intercept    (xy) =
Mar 3rd, 2015

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). 

Mar 4th, 2015

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