Key Features of Quadratic Functions

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, represented as an ordered pair (h, k) in the vertex form y = a(x - h)² + k.

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 equation x = h, where (h, k) is the vertex.

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 does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it means the coefficient of the x² term (a) is positive, indicating that the vertex is a minimum point.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, it means the coefficient of the x² term (a) is negative, indicating that the vertex is a maximum point.

Front

How do you find the vertex of a quadratic function in standard form?

Back

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

Front

What is the significance of the ordered pair (1, -2) in a quadratic function?

Back

If (1, -2) is the vertex, it represents the maximum or minimum point of the parabola, depending on whether it opens upwards or 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 the set of all y-values greater than or equal to the y-coordinate of the vertex, expressed as [k, ∞) where (h, k) is the vertex.

Front

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

Back

The range is the set of all y-values less than or equal to the y-coordinate of the vertex, expressed as (-∞, k] where (h, k) is the vertex.