10
AssignmentMultiple Select

Completing the Square

Question 10 • *Integrated Math II Full

Which functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply.

Answer
A
p(x) = 14(x + 7)2 + 1
B
q(x) = –5(x + 10)2 – 1
C
s(x) = –(x – 1)2 + 0.5
D
g(x) = 2x2 + 10x – 35
E
t(x) = –2x2 – 4x – 3

Explanation

A parabola has a maximum when it opens downward, so its squared-term coefficient must be negative. In vertex form, the vertex also shows the shifts: B has vertex (-10, -1), so it moves left and down; E can be rewritten as -2(x + 1)^2 - 1, giving vertex (-1, -1). Both have a maximum and are shifted left and down from f(x) = x².

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