10
QuizMultiple Choice

Completing the Square — Quiz

Question 10 • Algebra I

Which statements are true about the graph of the function f of x is equal to 6 x minus 4 plus x squared ? Choose two correct answers.

Answer
A
The axis of symmetry for the function is x is equal to 3 .
B
The vertex of the function is negative 3 comma negative 13 .
C
The vertex form of the function is f of x is equal to open paren x minus 2 close paren squared plus 2 .
D
The function does not cross the x -axis.
E
The graph increases over the interval negative 3 comma infinity .

Explanation

Complete the square: f(x) = x² + 6x − 4 = (x + 3)² − 13. This gives the vertex (−3, −13), so statement E is true. Since the parabola opens upward, it increases to the right of its vertex, over the interval (−3, ∞), making statement C true.

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