((p^2)-pq) - ((q^2)-pq)
(p^2) - (q^2) - 2pq
Problem 9
The instructions aren't stated anywhere, but I'm assuming your teacher wants you to find the equation of each parabola.
The vertex here is (h,k) = (-6,-4) which you have correctly determined.
This means

Next we plug in one of the other points on the parabola. We cannot pick the vertex again. Let's pick the point (-4,0) which is one of the x intercepts. We'll do this to solve for 'a'

This means

represents the equation of the parabola in vertex form.
<h3>Answer:

</h3>
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Problem 10
The vertex is (h,k) = (-2,-6)
So,

Now plug in another point on the parabola like (-1,-8) and solve for 'a'

<h3>Answer:

</h3>
For each equation, you could optionally expand things out to get it into y = ax^2+bx+c form, but I think it's fine to leave it as vertex form.
Factor
36-n^2 is difference of 2 perfect squares
a^2-b^2=(a-b)(a+b)
6^2-n^2=(6-n)(6+n)
factor
n^2+16n+60
find what 2 numbers multiply to 60 and add to 16
factors of 60=2,2,3,5
the numbers are 10 and 6
so factored out
(x+6)(x+10)
(x+6)=(6+x)
so the equation is
[(x+6)(x+10)]/[(6+x)(6-x)]=[(6+x)/(6+x)] times (x+10)/((6-x)=1 times (x+10)/(6-x)
the answer is (x+10)/(6-x)
Answer:
12a^2+18ab-6ac+25a-3b+c
Step-by-step explanation: