Algebra 2 - write the equation of the parabola in vertex form? Help!

Hi I'm new to this forum! I'm in Algebra 2 and I have a midterm to take tomorrow and I really need help with this problem!

It says:

"Suppose a parabola has vertex (-8, -7) and also passes through the point (-7, -4). Write the equation of the parabola in vertex form."

and the choices are:

a. y = (x+8)^2 - 7
b. y = 3(x-8)^2 -7
c. y = 3(x+8)^2 - 7
d. y = 3(x+8)^2 +7

Also, if you could just tell me how you got the answer, that'd be great. I'm just looking over my past tests because my math teacher said that's what the midterm will test us on, and I got this problem wrong. So the answer isn't b. Could anyone explain why?

Thanks,
Brooke

Substitute both points and see into which equation they fit.

emakarov - Is it choice a?

Substituting (-7, -4) into (a) gives -4 = (-7 + 8)^2 - 7 = 1 - 7 = -6. (A buzzer sound.)

Uh, ok? I just need to know how to get to the correct answer. I really struggle with math and I'm running short on time and I would love to just move on. Could anyone explain it to me? Thanks

Don't be lazy. Just substitute the numbers into the equations and calculate.

Quote:

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Originally Posted by wakefuldoze

...
It says:

"Suppose a parabola has vertex (-8, -7) and also passes through the point (-7, -4). Write the equation of the parabola in vertex form."

and the choices are:

a. y = (x+8)^2 - 7
b. y = 3(x-8)^2 -7
c. y = 3(x+8)^2 - 7
d. y = 3(x+8)^2 +7

...

---

Quote:

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Originally Posted by wakefuldoze

Uh, ok? I just need to know how to get to the correct answer. ...

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1. The equation of a parabola with the vertex $\displaystyle V(x_V, y_V)$ and the coefficient a is:

$\displaystyle y = a(x-x_V)^2+y_V$

2. Replace the coordinates of the vertex and you'll get:

$\displaystyle y = a(x+8)^2-7$

3. The coordinates of the given point have to satisfy this equation:

$\displaystyle -4=a(-7+8)^2-7$

Solve for a.

Thanks earboth!

Also, for this other problem:
"What steps transform the graph of y = x^2 to y = -(x+3)^2 + 5"

The choices are:

a. translate 3 units to the right, translate down 5 units
c. reflect across the x-axis, translate 3 units to the left, translate up 5 units
d. reflect across the x-axis, translate 3 units to the right, translate down 5 units

When is do you reflect across the x-axis? And I'm guessing that it's either a or d? Any help? Thank you to anyone who helps me! :)

Wait no, I bet it's c. Is it?

Yes, it's c.