Question

Let f(x)=x^2+2x+3 .

What is the average rate of change for the quadratic function from x=−2 to x = 5?

Answer 1

First you want to find the y values for when x=-2 and x=5
Substitute them into the equation to find y

Answer 2

still confused

Answer 3

\(\overline{\Delta}= \dfrac{f(b) - f(a)}{b - a}\)

Answer 4

Let b = 5 and a = -2 in this case

Answer 5

the average rate of change is another word for slope, also known as rise/run, also known as the variable 'm'. They all mean the same thing; the pattern of the function shift in relation to x and y. so as hero said the equation for this is (f(b)-f(a))/(b-a). the variable 'a' refers to the first value in the pair of intervals in this case the interval is (-2,5) and a=-2. so everywhere u see 'a' in that equation you can replace it with -2, make the b=5 and substitute it just like the 'a'. Now you should have (f(5)-f(-2))/(5-(-2)). Okay now evalute f(5) and f(-2); you can do this by simply plugging in 5 for x in the original equation, x^2+2x+3. that value you get will represent the y value where x=5, but thats not important after you find f(5) and f(-2) subtract those values and you should get 35/(5-(-2)). By this point in math you should know double negatives=positive giving you 35/7. You should find that the avr rate of change for x^2+2x+3equals 5

Answer 6

its alot i know but if you read it all i doubt you will be confused after