Key Features of Quadratic Functions

Front

Define Maximum

Back

The highest y-value on the graph.

Front

Define X-intercept

Back

Where the parabola touches or intersects the x-axis.

Front

Determine the domain and range of the function: y = ax^2 + bx + c

Back

Domain: All real numbers, Range: y ≥ minimum value (if a > 0) or y ≤ maximum value (if a < 0).

Front

Define Axis Of Symmetry

Back

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

Front

What is the vertex of a quadratic function?

Back

The highest or lowest point on the graph, represented as (h, k) in the vertex form y = a(x-h)^2 + k.

Front

What is the standard form of a quadratic function?

Back

y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a).

Front

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

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the vertex form of a quadratic function?

Back

y = a(x-h)^2 + k, where (h, k) is the vertex.