Question

Let f(x)=x2 2x 3. What is the average rate of change for the quadratic function from x=−2 to x = 5? Enter your answer in the box.

Answer 1

The average rate of change for the quadratic function x²+2x+3 from x=−2 to x = 5 is 5.

What is Slope?

A slope is also known as the gradient of a line or the average rate of change of a number that helps to know both the direction and the steepness of the line.

The rate of change of any function is the slope of the function, therefore, the slope of the function is written as,

$m = \dfrac{y_2 - y_1}{x_2-x_1}$

As the value of the y is the function of the x, while the value of x is given, therefore,

$x_2 = 5\\x_1=-2$

Now, the value of y,

$y_2 = f(5) = x^2 +2x+3 = (5)^2+2(5)+3 = 38\\y_1 = f(-2) = x^2 +2x+3 = (-2)^2+2(-2)+3 = 3$

Substituting the value of x and y in the formula of the slope, we can write the slope as,

$m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{f(x=5) - f(x=-2)}{5-(-2)}\\\\m = \dfrac{38-3}{7}\\\\m= 5$

Hence, the average rate of change for the quadratic function x²+2x+3 from x=−2 to x = 5 is 5.

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