Which of the following is the vertex form for the quadratic equation y = x2 − 18x + 70?
A. y = (x − 9)2 − 61
Incorrect. Did you remember to square half of b?
B. y = (x − 18)2 + 11
Incorrect. Half the x’s will be used for the length of the square and half will be used for the width.
C. y = (x − 9)2 + 70
Incorrect. Remember to add half of b squared to both sides.
D. y = (x − 9)2 − 11
Correct! You completed the square correctly.
Which of the following is the vertex for the function y = -2x2 − 4x − 10?
A. (-1, -8)
Correct! You completed the square correctly.
B. (1, 8)
Incorrect. Did you factor out -2?
C. (-1, 11)
Incorrect. After completing the square, did you distribute?
D. (2, -8)
Incorrect. Correctly complete the square to put the equation in vertex form. The vertex is (h, k).
Which of the following is not a perfect square?
A. (x − 1)2
Incorrect. This is a perfect square.
B. x2 + 2x + 2
Correct!
C. (4x − 9)2
Incorrect. This is a perfect square.
D. x2 + 6x + 9
Incorrect. This is a perfect square.
What is the x-value of the vertex of the equation y = 4x2 + 24x − 3?
A. -3
Correct!
B. -39
Incorrect. This is the y-value.
C. 9
Incorrect. Use -b 2a to find the x-value.
D. 38
Incorrect. You added 36 to -3 when you should have subtracted 33 from -3.
What number should be added to the expression x2 + 10x to complete the square?
A. 5
Incorrect. You forgot to square 5.
B. 20
Incorrect. You need to divide 10 by 2 and then take the square of the result.
C. 25
Correct!
D. 100
Incorrect. You forgot to divide 10 by 2 before you took the square.