Question

Find the thex-coordinate of the vertex of the function given below.

Y=(x-5)(x+3)

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

What do I fill in?? For the problem?

Answer 6

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

Answer 7

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

Answer 8

Can you first expand the expression?

Answer 9

What does that mean??

Answer 10

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

Answer 11

Expand the expression you have, like the example above.

Answer 12

X^2-2x+3??

Answer 13

Check your constant term again.

Answer 14

5?

Answer 15

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

Answer 16

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

Answer 17

Do you agree?

Answer 18

Yes

Answer 19

Now, complete the square.

Answer 20

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

Answer 21

Do you know how to do that?

Answer 22

no

Answer 23

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

Answer 24

Do you follow what I did in that last step?

Answer 25

Yes

Answer 26

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

Answer 27

But I will get a constant k.

Answer 28

x^2+1+k?

Answer 29

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

Answer 30

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.

Answer 31

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

Answer 32

What is the value of h?

Answer 33

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

Answer 34

so what do I do??

Answer 35

Tell me the value of h.

Answer 36

1?

Answer 37

Correct, that's your x-coordinate.

Answer 38

So the answer is 1