8.1: Key Features of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written 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

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

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

Back

The 'a' value determines the direction of the parabola's opening: if 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upward or downward.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting that value back into the function to find the y-coordinate.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, and it passes through the vertex.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating the function at x = 0.

Front

What is the significance of the ordered pair (0, c) in a quadratic function?

Back

The ordered pair (0, c) represents the y-intercept of the quadratic function.

Front

What does it mean for a parabola to have a maximum value?

Back

A parabola has a maximum value if it opens downward, meaning the vertex is the highest point on the graph.