Key Characteristics of 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 does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on whether the parabola opens upwards or downwards.

Front

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

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, the graph opens upwards. If 'a' is negative, the graph opens downwards.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0, which gives the value of c in the standard form.

Front

What are the zeros (or roots) 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 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 range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What does it mean for a quadratic function to have a maximum value?

Back

A quadratic function has a maximum value if it opens downwards, meaning the vertex represents the highest point on the graph.

Front

What does it mean for a quadratic function to have a minimum value?

Back

A quadratic function has a minimum value if it opens upwards, meaning the vertex represents the lowest point on the graph.