SOLUTION: Convert this equation to standard form of a parabola: 5x^2+30x+24y=51 p.s dont linked your answers to youtube.com because my phone can't play videos on youtube. thanks

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Convert this equation to standard form of a parabola: 5x^2+30x+24y=51 p.s dont linked your answers to youtube.com because my phone can't play videos on youtube. thanks      Log On


   

Question 1041186: Convert this equation to standard form of a parabola:
5x^2+30x+24y=51
p.s dont linked your answers to youtube.com because my phone can't play videos on youtube. thanks
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
As a general model, you can do this from the equation using all variables, and then use the resulting formula result.

First, adjust the equation as given.
5x%5E2%2B30x-51=-24y
24y=-5x%5E2-30x%2B51
y=-%285%2F24%29x%5E2-%2830%2F24%29x%2B51%2F24
y=-%285%2F24%29x%5E2-%285%2F4%29x%2B17%2F8

Now is a good place to examine the rest all in symbols to get a formula.
system%28a=-5%2F24%2Cb=-5%2F4%2Cc=17%2F8%29

y=ax%5E2%2Bbx%2Bc
Continue by using Completing The Square.
y=a%28x%5E2%2B%28b%2Fa%29x%2Bc%2Fa%29
y=a%28x%5E2%2B%28b%2Fa%29x%2B%28b%2F%282a%29%29%5E2-%28b%2F%282a%29%29%5E2%2Bc%2Fa%29
Watch and check through the next step carefully...
y=a%28%28x%2B%28b%2F%282a%29%29%29%5E2%2Bc%2Fa-%28b%5E2%29%2F%284a%5E2%29%29
Now distribute the factor, "a"...
y=a%28x%2B%28b%2F%282a%29%29%29%5E2%2Bc-%28b%5E2%29%2F%284a%29-----which may be useful enough this way or you could keep going like this....

(...bad rendered lines now fixed...)

*---
a%28x%2Bb%2F%282a%29%29%5E2%2Bc%28%284a%29%2F%284a%29%29-%28b%5E2%29%2F%284a%29

a%28x%2Bb%2F%282a%29%29%5E2%2B4ac%2F%284a%29-b%5E2%2F%284a%29

highlight%28y=a%28x%2Bb%2F%282a%29%29%5E2%2B%284ac-b%5E2%29%2F%284a%29%29

Look back to the variable assignments made above for a, b, and c. Make those substitutions now, and simplify, but KEEP your final result IN STANDARD FORM.

Note also, if you understand the process just shown, you could do the same thing starting from y=-%285%2F24%29x%5E2-%285%2F4%29x%2B17%2F8. I would not want to using your example; I would prefer to find a formula and then plug the values I need..... and then simplify as a last set of steps.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Convert this equation to standard form of a parabola:
5x^2+30x+24y=51
p.s dont linked your answers to youtube.com because my phone can't play videos on youtube. thanks
5x%5E2+%2B+30x+%2B+24y+=+51

The standard form of a parabolic equation is: f%28x%29+=+ax%5E2+%2B+bx+%2B+c

Therefore, 5x%5E2+%2B+30x+%2B+24y+=+51

24y+=+-+5x%5E2+-+30x+%2B+51

y+=+-+%285%2F24%29x%5E2+-+%2830%2F24%29x+%2B+%2851%2F24%29______highlight_green%28f%28x%29+=+-+%285%2F24%29x%5E2+-+%285%2F4%29x+%2B+17%2F8%29



If what you meant was the VERTEX form of a VERTICAL parabolic equation (f%28x%29+=+a%28x+-+h%29%5E2+%2B+k), then that's a different "story."