Advanced MathMediumCompleting a perfect square
Advanced Math practice question
The expression x² + 8x + c is equal to (x + k)² for all x, where c and k are constants. What is the value of c?
Answer: 16
(x + k)² = x² + 2kx + k². Matching 2k = 8 gives k = 4, so c = k² = 16.
Common wrong answers
- If you answered 4
- 4 is k, not c = k².
- If you answered 8
- 8 is the coefficient b, not c.
- If you answered 64
- 64 is 8², squaring the whole coefficient instead of half of it.
More Advanced Math questions
- Medium
What are the solutions to x² − 5x + 6 = 0? - Medium
The graph of f(x) = (x − 3)² + 4 is a parabola. What are the coordinates of its vertex? - Medium
If x² − 2x − 8 = (x + 2)(x − a), what is the value of a? - Medium
If √(x + 5) = 4, what is the value of x? - Medium
If f(x) = x + 3 and g(x) = 2x, what is f(g(4))? - Medium
What are the solutions to x² + 6x + 8 = 0?
Not affiliated with the College Board. SAT is a trademark of the College Board.