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 = ax^2 + bx + c, the vertex can be found using the formula (-b/2a, f(-b/2a)).

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.

Front

What does it mean if a quadratic function has a maximum value?

Back

A quadratic function has a maximum value when it opens downwards (a < 0). The vertex represents the maximum point.

Front

What does it mean if a quadratic function has a minimum value?

Back

A quadratic function has a minimum value when it opens upwards (a > 0). The vertex represents the minimum point.

Front

What is the y-intercept of 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.

Front

What is the general form of a quadratic function?

Back

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

Front

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

Back

If the coefficient 'a' in the quadratic function y = ax^2 + bx + c is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as (-∞, ∞).

Front

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

Back

The range is from the y-coordinate of the vertex to positive infinity, represented as [k, ∞) where (h, k) is the vertex.

Front

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

Back

The range is from negative infinity to the y-coordinate of the vertex, represented as (-∞, k] where (h, k) is the vertex.