Advanced MathMediumUsing a parabola's symmetry to find a second input
Advanced Math practice question
The function f is defined by f(x) = −2x² + 8x + 1. For what value of x other than 0 is f(x) equal to f(0)?
Answer: 4
f(x) = f(0) means −2x² + 8x = 0 → −2x(x − 4) = 0 → x = 4. (The axis of symmetry is x = 2, and 4 is the mirror of 0.)
Common wrong answers
- If you answered 1
- 1 is f(0), not an input.
- If you answered 2
- 2 is the axis of symmetry, where f is at its maximum, not where f equals f(0).
- If you answered 8
- 8 is the coefficient of x.
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.