*Solved .... doh!* Parabola word problem

[torrobinson]

I have the unit final tomorrow... I'm in grade 11.

We've been doing y=a(x-p)^2+q word problems... like giving the vertex and 2 points the parabola hits and finding it's equation.

However, I have 2 questions on the review sheet I cannot get:

Write the equation of a parabola that's vertex is (-1,7) and passes through (1,-5)

I did:
y=a(x-p)^2+q
-5=a(1+1)^2+7
-5=a+7
-12=a

Wririntg down the equation is no problem, but the key at the back of the review sheet says that "a" is actually -3 ....

and one more:



write the equation for a parabola with a vertex at (2,5), is congruent to y=5x^2, and opens down.

So I have "a" as -5
and "q" and "p" as the vertex....

So I write down

y=-5(x-2)^2+5

and have no idea how to know find "a"...

Help appreciated

 

[tkhunny]

\(\displaystyle 1+1 = 2\)

\(\displaystyle 2^{2} = 4\)

\(\displaystyle \frac{-12}{4} = -3\)

What does "congruent" mean in this context? Is 'a' different, or does your congruence require that it is the same?

 

[torrobinson]

Oh poop do I feel stupid.... I saw 1+1 and just thought "1" .... thanks! :roll:

She taught us that congruent meant same size... so it will be stretched at a factor of 5. And since it opens down, it will be a negative...

 

[tkhunny]

No need for such language or for feeling stupid. We're all learning. It's just your turn. Good work.

 

[torrobinson]

No need for such language or for feeling stupid. We're all learning. It's just your turn. Good work.

Sorry

...but I-

Wow... I posted this to ask about the second question to find I had already answered it and was trying to find x or y or something for some reason when all I needed was A, P,, and Q..... I was execting something harder.... now I feel even more stupid