Answer:
-4
Step-by-step explanation:
Average rate of change: y / x = (f(x₁) - f(x₂)) / (x₁ - x₂)
Note: it does not matter which goes first- x₁ or x₂. Just keep them in the same order for both parts (just like when you find slope)
For example, if we were conducting a lab experiment and there was 40 rats in week 2 and 80 rats in week 4, then to find the average rate of change:
(40 - 80) / (2 - 4) = -40 / -2 = 20 rats per week
Now, let's apply this to the equation we have.
h(x) = -x² + 3x + 1 when x=2 and x= 5
When x = 2,
-x² + 3x + 1 = - 2² + 3*2 + 1 = -4 + 6 + 1 = 3
When x = 5,
-x² + 3x + 1 = -5² + 3*5 + 1 = -25 + 15 + 1 = -9
Now, plug these into the equation (f(x₁) - f(x₂)) / (x₁ - x₂)
Let's set x₁ as 2 and x₂ as 5. So,
(h(2) - h(5)) / (2 - 5)
Then, substitute h(2) and h(5) with the numbers we already know.
(3 - (-9)) / (2 - 5)
12 / (-3) = -4
Thus, the answer is -4
I hope this helps! Feel free to ask any questions!
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