Answer:
1. [tex]y=(x+3)^2-4[/tex]
2. [tex]y=(x+4)^2-3[/tex]
3. [tex]y=(x-3)^2+4[/tex]
4. [tex]y=(x-4)^2+3[/tex]
Step-by-step explanation:
The vertex from of a quadratic function is
[tex]y=a(x-h)^2+k[/tex]
where, a is constant and (h,k) is vertex.
(1)
The vertex of the parabola is (-3,-4).
[tex]y=a(x-(-3))^2+(-4)[/tex]
[tex]y=a(x+3)^2-4[/tex]
The graph is passes through the point (-1,0).
[tex]0=a(-1+3)^2-4[/tex]
[tex]4=4a[/tex]
[tex]1=a[/tex]
[tex]y=(1)(x+3)^2-4[/tex]
[tex]y=(x+3)^2-4[/tex]
Therefore, the required equation is [tex]y=(x+3)^2-4[/tex].
Similarly,
(2)
The vertex of the parabola is (-4,-3).
[tex]y=a(x+4)^2-3[/tex]
The graph is passes through the point (-3,-2).
[tex]-2=a(-3+4)^2-3[/tex]
[tex]a=1[/tex]
Therefore, the required equation is [tex]y=(x+4)^2-3[/tex].
(3)
The vertex of the parabola is (3,4).
[tex]y=a(x-3)^2+4[/tex]
The graph is passes through the point (2,5).
[tex]5=a(2-3)^2+4[/tex]
[tex]a=1[/tex]
Therefore, the required equation is [tex]y=(x-3)^2+4[/tex].
(4)
The vertex of the parabola is (4,3).
[tex]y=a(x-4)^2+3[/tex]
The graph is passes through the point (3,4).
[tex]4=a(3-4)^2+3[/tex]
[tex]a=1[/tex]
Therefore, the required equation is [tex]y=(x-4)^2+3[/tex].
