Question

Question

Find the slope of the secant line between x
-3 and x = 5 on the graph of the function f(x) = -2x²-x+5.

Answer 1

Answer:5

Step-by-step explanation:To find the slope of the secant line between x=2x=2and x=5x=5on the graph of the function f(x)=x2−2x+5f(x)=x2−2x+5, you can use the formula for the average rate of change:Slope of Secant Line = f(5)−f(2)5−25−2f(5)−f(2)​First, calculate f(5)f(5)and f(2)f(2):f(5)=52−2(5)+5=25−10+5=20f(5)=52−2(5)+5=25−10+5=20f(2)=22−2(2)+5=4−4+5=5f(2)=22−2(2)+5=4−4+5=5Now, plug these values into the formula for the slope of the secant line:Slope of Secant Line = 20−55−2=153=55−220−5​=315​=5So, the slope of the secant line between x=2x=2and x=5x=5on the graph of the function is 5.

Answer 2

slope = 15

Explanation:

substitute x = - 3 and x = - 5 into f(x)

f(- 3) = - 2(- 3)² - (- 3) + 5

= - 2(9) + 3 + 5

= - 18 + 8

= - 10

then ( - 3, - 10) is one end of the secant

f(- 5) = - 2(- 5)² - (- 5) + 5

= - 2(25) + 5 + 5

= - 50 + 10

= - 40

then (- 5, - 40) is the other end of the secant

to find the slope m use the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (- 3, - 10 ) and (x₂, y₂ ) = (- 5, - 40 )

m =
`(-40-(-10))/(-5-(-3))` =
`(-40+10)/(-5+3)` =
`(-30)/(-2)` = 15