SOLUTION: Sketch the graphs, using the given roots to determine the function and the turning point. b. x = -8, x = -6

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Question 118382: Sketch the graphs, using the given roots to determine the function and the turning point.
b. x = -8, x = -6
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

or Start with the given roots

or Add 8 to both sides for the first equation. Add 6 to both sides for the second equation.

Now use the zero product property in reverse. Remember the zero product property says that if then or

Now foil. note: Let me know if you need help with foiling.

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Now to find the turning point, we need to find the x-coordinate of the turning point. To do that, simply use this formula:

So from we can see that and .

Plug and into the formula.

Multiply

Reduce

So the x-coordinate of the turning point is

Now we have to evaluate to determine the y-coordinate of the turning point.

Start with the given function.

Plug in . In other words, replace each x with -7.

Evaluate to get 49.

Multiply 14 and -7 to get -98

Now combine like terms

So the turning point is at (-7,-1)

Notice if we graph , we can see that the roots are and . We can also see that the turning point is (-7,-1). So this visually verifies our answer.