Key Features of Quadratic Functions

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. For example, in the function y = (x - 0)^2 + 18, the vertex is (0, 18).

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. It can be found using the formula x = -b/(2a) from the standard form of the quadratic equation y = ax^2 + bx + c.

Front

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

Back

A quadratic function has an absolute minimum if it opens upwards (a > 0) and the vertex represents the lowest point on the graph.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis. It can be found by evaluating the function at x = 0.

Front

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

Back

The range is the set of all possible output values (y-values). For a function that opens upwards with vertex (h, k), the range is y ≥ k.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by setting the quadratic equation equal to zero and solving for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of the quadratic equation ax^2 + bx + c = 0.

Front

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

Back

A quadratic function has a maximum if it opens downwards (a < 0) and the vertex represents the highest point on the graph.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.