Key Features of Quadratic Functions

Front

Define Axis Of Symmetry

Back

A line that divides the graph into two equal parts, cutting the graph in half.

Front

What are the x-values called?

Back

Domain

Front

What is the highest or lowest point on the graph of a quadratic function?

Back

Vertex

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the 'a' value in a quadratic function determine?

Back

The direction of the parabola (upward if a > 0, downward if a < 0).

Front

What are the x-intercept(s) of a quadratic function?

Back

The points where the graph intersects the x-axis.

Front

How do you find the vertex of a quadratic function in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the range of a quadratic function that opens upwards?

Back

[k, ∞) where k is the minimum value (y-coordinate of the vertex).

Front

What is the range of a quadratic function that opens downwards?

Back

(-∞, k] where k is the maximum value (y-coordinate of the vertex).

Front

What is the significance of the discriminant in a quadratic equation?

Back

It determines the nature of the roots: positive for two real roots, zero for one real root, negative for no real roots.