anonymous
  • anonymous
Find the thex-coordinate of the vertex of the function given below. Y=(x-5)(x+3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
The easiest way to determine the coordinates of the vertex is to write the parabola in vertex form.
anonymous
  • anonymous
Meaning, \[y = a(x-h)^2+k\]
anonymous
  • anonymous
You will have to expand that expression, then complete the square to get the vertex form.

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More answers

anonymous
  • anonymous
You will be able to read off the coordinates of the vertex (h, k) in the vertex form.
anonymous
  • anonymous
What do I fill in?? For the problem?
anonymous
  • anonymous
I listed the steps above. First, expand the expression. Then, complete the square.
anonymous
  • anonymous
I don't know what that means I need to find the a,h,x,k
anonymous
  • anonymous
Can you first expand the expression?
anonymous
  • anonymous
What does that mean??
anonymous
  • anonymous
(x+1)(x+2) = x^2 +3x + 2
anonymous
  • anonymous
Expand the expression you have, like the example above.
anonymous
  • anonymous
X^2-2x+3??
anonymous
  • anonymous
Check your constant term again.
anonymous
  • anonymous
5?
anonymous
  • anonymous
You multiply (x-5) by (x+3) right? You should get -5*3 = -15.
anonymous
  • anonymous
\[Y = (x-5)(x+3) = x^2-2x -15\]
anonymous
  • anonymous
Do you agree?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Now, complete the square.
anonymous
  • anonymous
This means you need to factorize the expression so that you force it to become a square (x+a)^2
anonymous
  • anonymous
Do you know how to do that?
anonymous
  • anonymous
no
anonymous
  • anonymous
\[x^2-2x-15= (x-1)^2+k\]
anonymous
  • anonymous
Do you follow what I did in that last step?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
I was able to factorize it into (x-1)^2 because of the -2x term.
anonymous
  • anonymous
But I will get a constant k.
anonymous
  • anonymous
x^2+1+k?
anonymous
  • anonymous
No, it's (x-1)^2+k
anonymous
  • 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
  • anonymous
Match the equation that we have, with the vertex formula above.
anonymous
  • anonymous
What is the value of h?
anonymous
  • anonymous
\[Y = a(x-h)^2+k =(x-1)^2+k\]
anonymous
  • anonymous
so what do I do??
anonymous
  • anonymous
Tell me the value of h.
anonymous
  • anonymous
1?
anonymous
  • anonymous
Correct, that's your x-coordinate.
anonymous
  • anonymous
So the answer is 1

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