Question

Write the quadratic function in the form g(x) = a (x-h)^2 +k.

Then, give the vertex of its graph.
g(x) = 2x^2 + 8x + 10

Answer 1

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Answer:

g(x) = 2(x +2)² +2

vertex: (-2, 2)

Explanation:

It is often easier to write the vertex form if the leading coefficient is factored from the variable terms:

g(x) = 2(x² +4x) +10

Then the square of half the x-coefficient is added inside parentheses, and an equivalent amount is subtracted outside.

g(x) = 2(x² +4x +4) +10 -2(4)

g(x) = 2(x +2)² +2

Comparing to the vertex form, we see the parameters are ...

a = 2, h = -2, k = 2

The vertex is (h, k) = (-2, 2).