SAT and ACT math terms · SAT Math, ACT Math
Quadratic function
Quadratic function: A function of the form f(x) = ax² + bx + c, whose graph is a parabola.
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What it means
If a > 0 the parabola opens upward and has a minimum; if a < 0 it opens downward and has a maximum. Standard form shows the y-intercept c. Factored form a(x − r)(x − s) shows the x-intercepts r and s. Vertex form a(x − h)² + k shows the vertex (h, k).
The axis of symmetry is x = −b/(2a), which is also the x-coordinate of the vertex.
Example
f(x) = (x − 2)(x + 4) has x-intercepts 2 and −4; the vertex's x-coordinate is halfway between them, at x = −1.
On the exam
SAT questions often ask which form displays a feature, such as the vertex or intercepts, as a constant or coefficient.
Lessons and practice questions
Related terms
- Vertex formThe form f(x) = a(x − h)² + k of a quadratic, which shows the vertex (h, k) directly.
- DiscriminantThe expression b² − 4ac in a quadratic equation ax² + bx + c = 0, which tells how many real solutions the equation has.
- Function notationWriting f(x) to show the output of function f for input x.