SOLUTION: Sketch the graphs, using the given roots to determine the function and the turning point. a. x = -2, x=4

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Question 118381: Sketch the graphs, using the given roots to determine the function and the turning point.

a. x = -2, x=4
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

or Start with the given roots

or Add 2 to both sides for the first root. Subtract 4 from both sides for the second root.

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.

So the function with roots of or is

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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

Negate -2 to get 2

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 1.

Evaluate to get 1.

Multiply -2 and 1 to get -2

Now combine like terms

So the turning point is (1,-9)

Notice if we graph , we can see that the roots are and . We can also see that the turning point is (1,-9). So this visually verifies our answer.