SOLUTION: How do I find the parabola of y=3x^2+4x-5

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Question 15: How do I find the parabola of y=3x^2+4x-5
Found 2 solutions by AnlytcPhil, KMST:
Answer by AnlytcPhil(1814) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find the parabola of y=3x2+4x-5
`
First you find some points:
`
`x| `y `| (x,y)
-3|`10 `|(-3,10)
-2|`-1 `|(-2,-1)
-1|`-6 `|(-1,-6)
`0|`-5 `|(0,-5)
`1| `2 `| (1,2)
`2|`15 `|(2,15)
Then you plot them and draw a smooth curve
graph%28200%2C200%2C-5%2C3%2C-16%2C16%2C3x%5E2%2B4%2Ax-5%29
Edwin

Answer by KMST(5456) About Me  (Show Source):
You can put this solution on YOUR website!
Quadratic functions are polynomials of degree 2.
They graph as parabolas, and they derive from y=x%5E2 graph%28100%2C100%2C-3%2C3%2C-1%2C5%2Cx%5E2%29 , with
maybe some stretching, graph%28100%2C200%2C-3%2C9%2C-1%2C11%2Cx%5E2%29 as in y=2x%5E2
maybe some flipping, as in y=-x%5E2 ,graph%28100%2C100%2C-3%2C3%2C-5%2C1%2C-x%5E2%29 ,
maybe some shifting, up and/or sideways, as in y=%28x-1%29%5E2%2B1 , graph%28100%2C100%2C-2%2C4%2C-1%2C5%2C%28x-1%29%5E2%2B1%29 ,
or all of the above.
We just need to get an equivalent expression of the form y=a%28+x+%2B-+h+%29%5E2+%2B-+k
y=3x%5E2%2B4x-5 --> y=3%28x%5E2%2B4x%2F3%29-5
I want to make %28X%2B2%2F3%29%5E2=x%5E2%2B4x%2F3%2B4%2F9 appear in the function expression.
y=3%28x%5E2%2B4x%2F3%2B4%2F9-4%2F9%29-5 --> y=3%28x%5E2%2B4x%2F3%2B4%2F9%29%2B3%28-4%2F9%29-5 --> y=3%28x%2B2%2F3%29%5E2-4%2F3-5 y=3%28x%2B2%2F3%29%5E2-19%2F3
When x=-2%2F3 , %28x%2B2%2F3%29%5E2=0 , and y=3%2A0-19%2F3=-19%2F3=-6%261%2F3
For any other value of x , %28x%2B2%2F3%29%5E2%3E0 , and y%3E-19%2F3 .
The parabola y=3x%5E2%2B4x-5 has a vertex at V%28-3%2F2%2C-19%2F3%29 and opens up: