what is the rate of change for the interval between 0 and 2 for the quadratic equation as (f(x)=2x^{2}+x…
what is the rate of change for the interval between 0 and 2 for the quadratic equation as (f(x)=2x^{2}+x - 3) represented in the table?\n-2 3\n-1 -2\n0 -3\n1 0\n2 7\n\\(\\frac{1}{5}\\)\n4\n5\n10
Answer
Explanation:
Step1: Recall rate - of - change formula
The rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$.
Step2: Identify $a$, $b$, $f(a)$ and $f(b)$
Here, $a = 0$, $b = 2$, $f(0)=-3$ and $f(2)=7$.
Step3: Calculate the rate of change
Substitute the values into the formula: $\frac{f(2)-f(0)}{2 - 0}=\frac{7-(-3)}{2}=\frac{7 + 3}{2}=\frac{10}{2}=5$.
Answer:
5