f(x) = −4x2 − 16x + 1
(b) Find its vertex and its x- and y-intercept(s). (If an answer does not exist, enter DNE.)
Using the quadratic formula the roots are given by:
x = [ -b +/- sqrt( b^2 - 4ac) ] 2a where a = -4, b = -16 and c = 1
x = -2 +/- sqrt(17)/2
So x-intercepts are (-2-sqrt(17)/2 , 0) and (-2+sqrt(17)/2 , 0).
y-intercept is simply (0, f(0)) = (0, 1)
The vertex form is given by y = a(x – h)^2 + k, where (h, k) is the vertex. We can calculate it using:
h = −b/2a = 16/8 = 2
k = c - b^2/4a = 1 - 16^2 / -16 = 17
So the vertex is (2,17).
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