Find the thex-coordinate of the vertex of the function given below.
Y=(x-5)(x+3)

- anonymous

Find the thex-coordinate of the vertex of the function given below.
Y=(x-5)(x+3)

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- anonymous

The easiest way to determine the coordinates of the vertex is to write the parabola in vertex form.

- anonymous

Meaning, \[y = a(x-h)^2+k\]

- anonymous

You will have to expand that expression, then complete the square to get the vertex form.

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## More answers

- anonymous

You will be able to read off the coordinates of the vertex (h, k) in the vertex form.

- anonymous

What do I fill in?? For the problem?

- anonymous

I listed the steps above. First, expand the expression. Then, complete the square.

- anonymous

I don't know what that means I need to find the a,h,x,k

- anonymous

Can you first expand the expression?

- anonymous

What does that mean??

- anonymous

(x+1)(x+2) = x^2 +3x + 2

- anonymous

Expand the expression you have, like the example above.

- anonymous

X^2-2x+3??

- anonymous

Check your constant term again.

- anonymous

5?

- anonymous

You multiply (x-5) by (x+3) right? You should get -5*3 = -15.

- anonymous

\[Y = (x-5)(x+3) = x^2-2x -15\]

- anonymous

Do you agree?

- anonymous

Yes

- anonymous

Now, complete the square.

- anonymous

This means you need to factorize the expression so that you force it to become a square (x+a)^2

- anonymous

Do you know how to do that?

- anonymous

no

- anonymous

\[x^2-2x-15= (x-1)^2+k\]

- anonymous

Do you follow what I did in that last step?

- anonymous

Yes

- anonymous

I was able to factorize it into (x-1)^2 because of the -2x term.

- anonymous

But I will get a constant k.

- anonymous

x^2+1+k?

- anonymous

No, it's (x-1)^2+k

- anonymous

Since you're only interested in the x-coordinate of the vertex, we are done. You don't need to solve for k in this question.

- anonymous

Match the equation that we have, with the vertex formula above.

- anonymous

What is the value of h?

- anonymous

\[Y = a(x-h)^2+k =(x-1)^2+k\]

- anonymous

so what do I do??

- anonymous

Tell me the value of h.

- anonymous

1?

- anonymous

Correct, that's your x-coordinate.

- anonymous

So the answer is 1

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