At the vertex, the function changes from increasing to decreasing, or vice versa.
Vertex form is an algebraic format used to express quadratic function rules.
From the graph, we can connect the following characterisitcs to the function rule.Notice that although the factor in the function rule shows is actually equal to This coincides with a horizontal translation of a quadratic function.
Quadratic function rules can be expressed in factored form, sometimes referred to as intercept form.
As is the case with standard form and vertex form, gives the direction of the parabola. When the parabola faces upward, and when it faces downward. Additionally, the zeros of the parabola lie at Because the points of a parabola with the same -coordinate are equidistant from the axis of symmetry, the axis of symmetry lies halfway between the zeros. Consider the graph of
From the graph, the following characteristics can be connected to the function rule.
For the following functions, determine the direction, the axis of symmetry, vertex, and zeros.
A function's rate of change gives an indication of how its outputs () change with respect to its inputs ().
When the rate of change is constant, the function is linear. However, when the function is not linear, it's possible to determine an average rate of change over an arbitrary interval. This is an increase or decrease between the endpoints of the interval. If the -coordinates of the endpoints are and and the function is the average rate of change is defined as follows.
The function is quadratic.
Determine the average rate of change over the interval
To determine the average rate of change, we must know the -values of the endpoints. Since the interval is the -values are and Let's mark these points on the graph to find their corresponding function values.