Advanced MathMediumUsing symmetry about a parabola's vertex
Advanced Math practice question
In the xy-plane, the graph of y = a(x − 2)² + 3 passes through the point (0, 11), where a is a constant. What is the y-coordinate of the point on the graph with x-coordinate 4?
Answer: 11
The axis of symmetry is x = 2, and 0 and 4 are equally far from it, so the y-values match: 11. (Indeed a = 2, and 2(4 − 2)² + 3 = 11.)
Common wrong answers
- If you answered 3
- 3 is the vertex's y-coordinate.
- If you answered 7
- 7 comes from a = 1.
- If you answered 19
- 19 comes from a = 2 with (4 − 2)² read as 8.
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.