- Vertex form: [tex] y=a(x-h)^2+k [/tex] , with (h,k) as the vertex.
For this, we will be using vertex form. Firstly, plug the vertex into the vertex form equation:
[tex] y=a(x-(-3))^2+1\\y=a(x+3)^2+1 [/tex]
Next, we need to solve for a. Plug in (-2,4) into the x and y coordinates to solve for a as such:
[tex] 4=a(-2+3)^2+1\\4=a(1)^2+1\\4=a+1\\3=a [/tex]
Putting our equation together, it's [tex] y=3(x+3)^2+1 [/tex]
*Additional section*
- Standard form: [tex] y=ax^2+bx+c [/tex]
Converting to standard form as such:
[tex] y=3(x+3)^2+1\\y=3(x^2+6x+9)+1\\y=3x^2+18x+27+1\\y=3x^2+18x+28 [/tex]
