Characteristics of Quadratic Functions

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis. For example, in the function with x-intercepts at 0 and 4, these are the values of x when y=0.

Front

Name the parent function of quadratic functions.

Back

The parent function of quadratic functions is the quadratic function itself, typically represented as f(x) = x².

Front

Using the graph of the quadratic function, how do you identify the vertex?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. For example, in the vertex (4, -6), 4 is the x-coordinate and -6 is the y-coordinate.

Front

How many solutions can a quadratic function have?

Back

A quadratic function can have zero, one, or two solutions, depending on the number of times the graph intersects the x-axis.

Front

What is a parabola?

Back

A parabola is the U-shaped graph of a quadratic function, which can open upwards or downwards.

Front

What is the standard form of a quadratic function?

Back

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

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the quadratic function, indicating the highest or lowest value of the function.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) in the standard form f(x) = ax² + bx + c.