Average Rate of Change of Quadratic Functions

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval [a, b] is defined as (f(b) - f(a)) / (b - a). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

Front

How do you calculate the average rate of change for a quadratic function?

Back

To calculate the average rate of change for a quadratic function f(x) = ax^2 + bx + c over an interval [a, b], use the formula: (f(b) - f(a)) / (b - a).

Front

What is the average rate of change of the function k(x) = x^2 - 6x + 9 over the interval [3, 5]?

Back

2

Front

Calculate the average rate of change of the function f(x) = 2x^2 - 3x + 5 over the interval [1, 3].

Back

5

Front

What is the average rate of change of the function m(x) = -2x^2 + 5x - 3 over the interval [0, 4]?

Back

-3

Front

Determine the average rate of change of the function p(x) = -x^2 + 3x - 2 over the interval [1, 4].

Back

4

Front

Calculate the average rate of change of the function r(x) = 5x^2 - 2x + 3 over the interval [-3, 3].

Back

40

Front

What does the term 'quadratic function' mean?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.