SAT Math: Vertex Form of a Quadratic
38+ practice questions in Praczo
The concept, explained
- 1
Vertex form is f(x) = a(x − h)² + k, where (h, k) is the vertex — the maximum or minimum point of the parabola.
- 2
a > 0: parabola opens upward, vertex is the minimum. a < 0: opens downward, vertex is the maximum.
- 3
Read the vertex directly from the equation: f(x) = 2(x − 3)² + 5 has vertex (3, 5). Watch the sign: the form is (x − h), so (x − 3) means h = +3.
- 4
The axis of symmetry is the vertical line x = h.
- 5
To convert from standard form ax² + bx + c, find h = −b/(2a), then compute k = f(h).
- ✗ Reading the vertex sign wrong: f(x) = (x + 3)² + 5 has vertex (−3, 5), not (+3, 5) — because (x + 3) = (x − (−3)), so h = −3.
- ✗ Confusing the axis of symmetry (a line: x = h) with the vertex (a point: (h, k)).
SAT-style practice
The function f(x) = −2(x − 4)² + 7 reaches a maximum. What is the maximum value and at what value of x does it occur?
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