Question

en the quadratic: ( y = x^2 - 5x + 13 ), find the average rate of change on (1,4).
given the linear function: ( y = -9x + 3 ), find the average rate of change on (-1,5).
given the linear function: ( y = 2x + 8 ), find the average rate of change on (3,5).
given the quadratic: ( y = x^2 + x - 3 ), find the average rate of change on .
given the quadratic: ( y = x^2 - 7x + 12 ), find the average rate of change on .

Explanation:

Step1: Find $y(3)$ for $y=2x+8$

$y(3)=2(3)+8=6+8=14$

Step2: Find $y(5)$ for $y=2x+8$

$y(5)=2(5)+8=10+8=18$

Step3: Apply average rate formula

$\text{Average rate of change}=\frac{y(5)-y(3)}{5-3}=\frac{18-14}{2}=\frac{4}{2}=2$

Answer:

2

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Note: The last two quadratic problems have incomplete interval information $[\quad]$. Please provide the full interval for $y=x^2+x-3$ and $y=x^2-7x+12$ to solve for their average rates of change.