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vladimir1956 [14]
3 years ago
9

Find the equation of the parable in general form by completing the square. Then, state its vertex

Mathematics
1 answer:
lora16 [44]3 years ago
6 0
The parabola will show the vertex in the format: y-k = (x-h)^2, where the vertex point
lies at (h, k).
so \: for \:  {x}^{2}  + 2x - y + 3 = 0
let's first put it in "y =" standard format:
y =  {x}^{2}  + 2x + 3
Since we cannot get a perfect square out of this, we complete the square: a=1, b=2, c=3
(b/2)^2 = (2/2)^2 = 1, so
y =  {(x +1)}^{2} ...\: is \: y =  {x}^{2}  + 2x + 1
So there's +2 leftover, since 3-1=2; so:
y =  {(x + 1)}^{2}  + 2
Now we'll subtract the 2 from both sides to show our vertex:
y - 2 =  {(x + 1)}^{2}
where our vertex (h, k) is at (-1, 2)
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