Answer:
[tex]y=(x+8)(x+10)=x^2 + 18x + 80[/tex]
[tex]\frac{dy}{dx} = 2x + 18[/tex]
[tex]y=0[/tex] when [tex]x=-8[/tex] and [tex]x=-10[/tex]
so the tangent slopes are [tex]\frac{dy}{dx} = 2[/tex] and -2 at those x.
The lines are y = 2x + b and y = -2x + c.
We need to find b and c.
The first line must go through (-8,0) and the second one through (-10,0).
For the first line: 0 = 2*(-8) + b and b = 16.
For the second line: 0 = -2*(-10) + c and c = -20.
Step-by-step explanation:
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