Advanced MathVery hardVertex from intercepts
Advanced Math practice question
In the xy-plane, the graph of the quadratic function g crosses the x-axis at (−1, 0) and (5, 0) and the y-axis at (0, −5). What is the y-coordinate of the vertex of the graph?
Answer: -9
g(x) = a(x + 1)(x − 5). From g(0) = −5: −5a = −5, so a = 1. The vertex is at x = 2, where g(2) = (3)(−3) = −9.
Common wrong answers
- If you answered 2
- 2 is the x-coordinate of the vertex.
- If you answered 9
- 9 has the sign wrong; the parabola opens upward, so the vertex is a minimum.
- If you answered -5
- −5 is the y-intercept, not the vertex.
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