<u>End behavior: </u>
The parent function is: f(x) = x³, which starts (from the left side) at -∞ and ends (on the right side) at +∞.
<u>Zeroes:</u>
f(x) = x³ + 2x² - 8x
0 = x³ + 2x² - 8x
0 = x(x² + 2x - 8)
0 = x(x + 4)(x - 2)
0 = x 0 = x + 4 0 = x - 2
x = 0 x = -4 x = 2
<u>Intervals:</u>
Put the zeroes in order: -4, 0, 2
since f(x) is increasing from the left then the interval from -4 to 0 is positive and the interval from 0 to 2 is negative.
<u>Graph:</u>
see attachment
Answer: Slope = 2/5
Concept:
Here, we need to know how to find the slope.
Slope = (y₂ - y₁) / (x₂ - x₁)
If you are still confused, please refer to the attachment below for a clearer version of the formula
Solve:
<u>Given information</u>
(x₁, y₁) = (-6, 2)
(x₂, y₂) = (4, 6)
<u>Given formula</u>
Slope = (y₂ - y₁) / (x₂ - x₁)
<u>Substitute values into the formula</u>
Slope = (6 - 2) / (4 - (-6))
<u>Simplify values in the parentheses</u>
<u>REMEMBER to change [+, -] signs when there is a [-] sign in front</u>
Slope = 4 / (4 + 6)
Slope = 4 / 10
<u>Divide both numerator and denominator by 2 to get the simplest form</u>
Slope = (4 ÷ 2) / (10 ÷ 2)
Slope = 2/5
Hope this helps!! :)
Please let me know if you have any questions
