Question

Find the standard form of the equation of the parabola with the given characteristics.
Vertex (3,-9) ; Focus (3,-7)

Answer 1

this may help... http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

Answer 2

Thanks!
The equation for the standard form of a parabola would be y=ax^2+bx+c, right? How do I incorporate the vertex and focus into that formula?

Answer 3

you have the vertex V(h,k) right?

Answer 4

Yes, h=3, k=-9

Answer 5

y-k = a(x-h)^2 for the vertex form at standard form y = ax^2 + bx + c
x-h = a(y-k)^2 for sideways wherein x=ay^2 + by + c

Answer 6

from the given points, the focus is 2 units above the vertex and both 3 units from x=0 line or simply the y-axis... thru these observations, we have a parabola which vertex and focus points located in the 4th quadrant and opens upward... :)

Answer 7

so we can use the vertex form
y-k = a (x-h)^2

Answer 8

a = 1/(4p) where p is the distance between the vertex and focus points

Answer 9

for a parabola that opens upward, a > 0...

Answer 10

substitute all known values to vertex form then work on the equation until you got the standard form of Quadratic Equation....

Answer 11

Oh okay! Thanks so much. And to be sure, p would equal 2 in this case because that's the distance right?

Answer 12

yup... you're right... :)

Answer 13

I'm at this point so far: y+9 = 1/8(x-3)^2. Am I on the right track?

Answer 14

yup you can continue...

Answer 15

Ty :)

Answer 16

I'm not sure if this is right but I got: 1/8x^2 - 3/4x+81/8

Answer 17

hmmm... there is something wrong with your simplification....

Answer 18

you have to work on both side of the equation
\[y+9=\frac{ 1 }{ 8 }(x-3)^2\]

Answer 19

Oh okay. So would we expand (x-3)^2 first?

Answer 20

we can start on that...

Answer 21

(x-3)(x-3) would be x^2-6x+9 right?

Answer 22

correct...

Answer 23

And then you multiply that by 1/8 and get: 1/8x^2 -3/4+9/8

Answer 24

you can have that, but much better we avoid fraction distribution, so to avoid doing how will we removed 1/8 on the right-hand side?

Answer 25

multiplying everything by 8? i think.

Answer 26

ok do it...

Answer 27

I have 8y=x^2-6x-63 so far.

Answer 28

now to follow the standard form of y=ax^2+bx+c...what must you do?

Answer 29

Divide both sides by 8 right? to isolate the y.

Answer 30

yup... then simplify further :)

Answer 31

\[y=x^2/8 - 6x/8 - 63/8\]

Answer 32

Hmmm, I'm not sure how to fix this haha

Answer 33

well it's all that we need... merely the simplified one...
\[y=\frac{ 1 }{ 8 }x^2-\frac{ 3 }{ 4 }x-\frac{ 63 }{ 8 }\]

Answer 34

Oh so thats the simplified answer?

Answer 35

congratulations you made it all by yourself.... :)

Answer 36

Thank you so much for your help!

Answer 37

no problem... anytime... :)