Graphing Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically 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 of the parabola represented by the quadratic function.

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 formula to find the vertex of a quadratic function?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

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 significance of the 'b' value in a quadratic function?

Back

The 'b' value affects the position of the vertex along the x-axis and the axis of symmetry.

Front

What is the significance of the 'c' value in a quadratic function?

Back

The 'c' value represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

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

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, found by evaluating f(0).