SOLUTION: please help me make this into standard form and show it in a graph with roots. {{{ 3x^2+x=-4x+5 }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: please help me make this into standard form and show it in a graph with roots. {{{ 3x^2+x=-4x+5 }}}      Log On


   

Question 871053: please help me make this into standard form and show it in a graph with roots. +3x%5E2%2Bx=-4x%2B5+
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify first.
3x%5E2%2B5x-5=0. The function would be something general as y=3x%5E2%2B5x-5=0. The term to complete the square is (5/2)^2, which you should ..... Not that.... but better, this...

y=3%28x%5E2%2B%285%2F3%29x%2B5%2F3%29=0. Now, using this might be better. The term to complete the square is %285%2F%282%2A3%29%29%5E2=%285%2F6%29%5E2.

y=3%28x%5E2%2B%285%2F3%29x%2B%285%2F6%29%5E2%2B5%2F3-%285%2F6%29%5E2%29
y=3%28%28x%2B5%2F6%29%5E2%2B5%2F3-%285%2F6%29%5E2%29
y=3%28x%2B5%2F6%29%5E2%2B3%285%2F3-%285%2F6%29%5E2%29
y=3%28x%2B5%2F6%29%5E2%2B3%2860%2F36-25%2F36%29
y=3%28x%2B5%2F6%29%5E2%2B3%2835%2F36%29
highlight%28y=3%28x%2B5%2F6%29%5E2%2B35%2F12%29. STANDARD FORM.

The vertex is a minimum, at (-5/6, 35/12). The roots will be found simply solving y=0. This is partly done already because the equation is now in standard form.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

please help me make this into standard form and show it in a graph with roots. +3x%5E2%2Bx=-4x%2B5+


3x%5E2+%2B+x+=+-+4x+%2B+5

3x%5E2+%2B+x+%2B+4x+-+5+=+0



Standard form of parabolic equation: highlight_green%28y+=+3x%5E2+%2B+5x+-+5%29

I'll graph the equation later, showing roots