9
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Completing the Square (Continued)

Question 9 • FL-1200700-Mathematics for College Algebra MIS

The function g(x) = 10x2 – 100x + 213 written in vertex form is g(x) = 10(x – 5)2 – 37. Which statements are true about g(x)? Select three options.The axis of symmetry is the line x = –5.The vertex of the graph is (5, –37).The parabola has a minimum.The parabola opens up.The value of a, when the equation is written in vertex form, is negative.

Answer
A
The axis of symmetry is the line x = –5.
B
The vertex of the graph is (5, –37).
C
The parabola has a minimum.
D
The parabola opens up.
E
The value of a, when the equation is written in vertex form, is negative.

Explanation

In vertex form, g(x) = a(x − h)² + k, the vertex is (h, k) and the axis of symmetry is x = h. Here, g(x) = 10(x − 5)² − 37, so the vertex is (5, −37), and the axis is x = 5, not x = −5. Since a = 10 is positive, the parabola opens up and has a minimum.

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