Answer:
[tex]y+2=2(x-1)^{2}[/tex] -----> vertex form
[tex]y=2x^{2}-4x[/tex] -----> standard form
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y-k=a(x-h)^{2}[/tex]
where
(h,k) is the vertex of the parabola
In this problem we have
[tex](h,k)=(1,-2)[/tex]
[tex]Point(3,6)[/tex]
substitute the values and solve for a
[tex]6-(-2)=a(3-1)^{2}[/tex]
[tex]8=a(2)^{2}[/tex]
[tex]8=a(4)[/tex]
[tex]a=2[/tex]
the equation in vertex form is equal to
[tex]y+2=2(x-1)^{2}[/tex]
Find the equation of the parabola in standard form
we know that
the equation of the parabola in standard form is equal to
[tex]y=ax^{2}+bx+c[/tex]
we have
[tex]y+2=2(x-1)^{2}[/tex]
convert to standard form
[tex]y+2=2(x^{2}-2x+1)\\ \\y+2= 2x^{2}-4x+2\\ \\y=2x^{2}-4x+2-2\\ \\y=2x^{2}-4x[/tex]
