8
QuizMultiple Choice

Completing the Square (Continued) — Quiz

Question 8 • Algebra I

Which statement is true concerning the vertex and the axis of symmetry of g of x is equal to 5 x squared minus 10 x ?

Answer
A
The vertex is at 0 comma 0 and the axis of symmetry is y is equal to 1 .
B
The vertex is at 0 comma 0 and the axis of symmetry is x is equal to 1 .
C
The vertex is at 1 comma negative 5 and the axis of symmetry is y is equal to 1 .
D
The function written in vertex form is g of x is equal to 5 times open paren x minus 1 close paren squared minus 5 . The vertex is at 1 comma negative 5 and the axis of symmetry is x is equal to 1 .

Explanation

Complete the square: g(x) = 5x² − 10x = 5(x² − 2x) = 5(x − 1)² − 5. In vertex form, the vertex is (1, −5), and the axis of symmetry is the vertical line x = 1. Therefore, the true statement is that the vertex form is 5(x − 1)² − 5, with vertex (1, −5) and axis x = 1.

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