Question

What are the coordinates of the vertex for f(x) = x2 + 4x + 10?

(2, 2)
(2,6)
(-2, 2)
(-2, 6)

Answer 1

9514 1404 393

Answer:

(d) (-2, 6)

Explanation:

We can rewrite the function using vertex form.

f(x) = (x^2 +4x) +10

f(x) = (x^2 +4x +4) +10 -4 . . . . . . . add and subtract (4/2)^2

f(x) = (x +2)^2 +6

Compare to vertex form:

f(x) = (x -h)^2 +k

we see that (h, k) = (-2, 6) . . . . the vertex

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Additional comment

The value added and subtracted is the square of half the x-coefficient. Inside parentheses, that value "completes the square". Outside parentheses, that value ensures the overall function remains unchanged.