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 does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient (a).

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 the parabola opens upwards or downwards.

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), where a and b are coefficients from the quadratic function in standard form.

Front

What is the significance of the leading coefficient in a quadratic function?

Back

The leading coefficient (a) determines the direction of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.

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 f(x) = 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 (3, 0) in a quadratic function?

Back

The ordered pair (3, 0) represents an x-intercept of the quadratic function.

Front

What is the significance of the ordered pair (0, -2) in a quadratic function?

Back

The ordered pair (0, -2) represents the y-intercept of the quadratic function.