Question 84554: How would I write an equation in standard form of a parabola with a line of symmetry x=2 and containing (2,3)(4,-5)?
Answer by vertciel(183)   (Show Source):
You can put this solution on YOUR website! Hello there,
There are three forms of the equation of a parabola. We will use the form y = a(x - k)^2 + k.
The line of symmetry for a parabola is where its x coordinate for the axis is located. The above form of the parabola requires the vertex and the general wideness of the parabola (a).
Since (2,3) is given, we know that the vertex of the parabola is at (2,3).
Our parabola thus:
y = a(x - 2)^2 + 3
Now we need to find a.
You can either substitute (4, -5) as x and y into that equation, or use the formula a = rise/run^2.
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