Question

Which is the best estimate for the average rate of change for the quadratic function graph on the interval 0 ≤ x ≤ 2?

Answer 1

The average rate of change of f on the interval 0 ≤ x ≤ 2 equals 4

Explanation:

You haven't provided any function, so I can't help you in an exact way. However, I'll help you choosing a quadratic function. This type of functions are given by the form:

$f(x)=ax^2+bx+c \\ \\ a,b,c \ real \ constants$

On the other hand, the average rate of change is defined as:

$ARC=\frac{Change \ in y}{Change \ in \ x} \\ \\ ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$

So, let's choose:

$f(x)=x^2+2x+4$

We have the interval:

$0\leq x\leq 2$

So:

$x_{1}=0 \\ \\ x_{2}=2 \\ \\ f(x_{1})=0^2+2(0)+4=4 \\ \\ f(x_{2})=2^2+2(2)+4=4+4+4=12$

$ARC=\frac{12-4}{2-0} \\ \\ ARC=\frac{8}{2} \\ \\ \boxed{ARC=4}$

Learn more:

Average Rate of Change: https://brainly.com/question/7666020

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