SOLUTION: Write the given expression f(x)= x^2+10x+7 in the form f(x)=a(x-h)^2+k. And identify the vertex

Question 335938: Write the given expression f(x)= x^2+10x+7 in the form f(x)=a(x-h)^2+k. And identify the vertex
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract . Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

So after completing the square, transforms to . So .

This means that is equivalent to .

So the equation is now in vertex form where , , and

Remember, the vertex of is (h,k).

So the vertex of is (-5,-18) since h=-5 and k=-18

This means that the vertex of is (-5,-18)

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my website.

Jim

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