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 and a ≠ 0.

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 is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

What does the axis of symmetry represent in a quadratic function?

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

How do 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 this value back into the function to find the y-coordinate.

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 (2, -4) in a quadratic function?

Back

It is the vertex of the graph.

Front

What does the range of a quadratic function indicate?

Back

The range indicates the possible output values (y-values) of the function, which depend on the vertex and the direction the parabola opens.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value is the y-coordinate of the vertex, representing the highest or lowest point of the graph.