8.1: Key Features of Quadratic Functions

Front

What is a quadratic function?

Back

A polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c, where a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph is a parabola, which can open upwards or downwards.

Front

What is the vertex of a parabola?

Back

The highest or lowest point on the graph of a quadratic function.

Front

How do you determine if a parabola opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic function is positive, it opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry in a parabola?

Back

A vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What are the x-intercepts of a quadratic function?

Back

The points where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

What is the y-intercept of a quadratic function?

Back

The point where the graph intersects the y-axis, found by evaluating f(0).

Front

What is the maximum value of a quadratic function?

Back

The highest point on the graph, occurring at the vertex if the parabola opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The lowest point on the graph, occurring at the vertex if the parabola opens upwards.