Characteristics of Quadratic Functions: Graphs

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 are the characteristics of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola that opens upwards if a > 0 and downwards if a < 0.

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

How do you find the axis of symmetry of 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 equation.

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the graph intersects the x-axis, found by solving the equation f(x) = 0.

Front

What is the maximum value of a quadratic function?

Back

The maximum value occurs at the vertex of the parabola when it opens downwards.

Front

What is the minimum value of a quadratic function?

Back

The minimum value occurs at the vertex of the parabola when it opens upwards.

Front

How can you determine if a quadratic function has two zeros?

Back

A quadratic function has two zeros if the discriminant (b² - 4ac) is greater than zero.

Front

What does it mean if a quadratic function has one zero?

Back

A quadratic function has one zero if the discriminant (b² - 4ac) is equal to zero, indicating the vertex touches the x-axis.

Front

What does it mean if a quadratic function has no zeros?

Back

A quadratic function has no zeros if the discriminant (b² - 4ac) is less than zero, indicating the graph does not intersect the x-axis.