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