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QuizMultiple Choice

Completing the Square — Quiz

Question 2 • Algebra I

Which statements are true about the graph of the function f of x is equal to x squared minus 8 x plus 5 ? Choose three correct answers.

Answer
A
The y -intercept of the function is 0 comma 5 .
B
The function in vertex form is f of x is equal to open paren x minus 4 close paren squared minus 11 .
C
The function crosses the x -axis twice.
D
The vertex of the function is negative 8 comma 5 .
E
The axis of symmetry is x is equal to 5 .

Explanation

Completing the square gives f(x) = (x − 4)² − 11, so choice C is true. The quadratic has two x-intercepts because its discriminant is (−8)² − 4(1)(5) = 44, which is positive, making B true. Setting x = 0 gives f(0) = 5, so the y-intercept is (0, 5), as in choice D. The vertex is (4, −11), and the axis of symmetry is x = 4, so A and E are false.

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