Write the equation of the parabola with vertex (2,-1) and a point (0,3). What is the equation for the axis?

Question

you would use the vertex form equation right?

Answer 1

THe vertex (h,k) is plugged into the equation y=a(x-h)+k
So at 2,-1 y=a(x-2)^2-1
To find the value of a plug in your x and y at (0,3)
3=a(0-2)^2-1
add one on both sides
4=(-2)^2a
4=4a
Divide by 4 on both sides
a=1
So your equation is
y=(x-2)^2-1
or y=x^2-4x+3

Answer 2

A parabola opening up or down with vertex at (a,b) as the equation
y = k(x - a)^2 +b

so your parabola can be written as

y = k(x-2)^2 -1

You only need to find k. But since you also know the point (0,3) is on the parbola you can put in 0 for x and 3 for y which will allow you to solve for k.

Good luck.

Answer 3

Vertex or standard form equation?

Vertex= a(x - h) ^2 - k
y = a (x -2)^2 - (-1)
y = a (x -2)^2 + 1
3 = a (0 - 2)^2 + 1
3= 4a + 1
2 = 4a
1/2 = a
Vertex= f(x) = 1/2 (x -2)^2 + 1
Standard = f(x) 1/2x^2 - 2x + 3

Answer 4

(x-2)^2 = 2p(y+1)
(0-2)^2 =2p(3+1)
4= 8p
p = .5
So final equation is (x-2)^2 = y+1, or
y = x^2-4x + 3