Quadratic Functions - Review Flashcards

Flashcards covering key concepts from Lessons 8.1 through 8.6, including graphing quadratic functions, finding zeros, and comparing different types of functions.

Axis of Symmetry (AOS)

A vertical line that divides the parabola into two symmetrical halves. For f(x) = ax² it is x=0.

Vertex

The point where the parabola changes direction; either a minimum or maximum point. For f(x) = ax², the vertex is (0,0).

Vertical Shrink

A transformation that makes the graph wider than the parent function. In the form y = ax², this occurs when |a| < 1.

Vertical Stretch

A transformation that makes the graph narrower than the parent function. In the form y = ax², this occurs when |a| > 1.

Vertical Translation

Shifting the graph up or down. In the form f(x) = ax² + c, the graph is shifted 'c' units up (if c is positive) or down (if c is negative).

Zeros of a Function

The x-values where the function's graph intersects the x-axis (where y=0). Found by setting y = 0 and solving for x.

Standard Form of a Quadratic Function

f(x) = ax² + bx + c, where a, b, and c are constants.

Axis of Symmetry (for f(x) = ax² + bx + c)

x = -b / 2a

Vertex Form of a Quadratic Function

f(x) = a(x − h)² + k, where (h, k) is the vertex of the parabola.

Intercept Form of a Quadratic Function

f(x) = a(x - p)(x - q), where p and q are the x-intercepts (zeros) of the function.

X-Intercepts

The points where the parabola intersects the x-axis; also known as zeros or roots of the quadratic function.

Linear Function

A function where the first difference between y-values is constant for equally spaced x-values.

Quadratic Function

A function where the second difference between y-values is constant for equally spaced x-values.

Exponential Function

A function where the y-values are multiplied by a constant factor for equally spaced x-values.