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Answer:
[tex]y = 2(x +3)^2 -2[/tex]
Step-by-step explanation:
Given
[tex](h,k) = (-3,-2)[/tex] --- vertex
[tex](x,y) = (-5,6)[/tex] --- point
Required
Determine the equation
The general form is:
[tex]y = a(x - h)^2 + k[/tex]
First, we solve for a:
Substitute [tex](h,k) = (-3,-2)[/tex] and [tex](x,y) = (-5,6)[/tex] in [tex]y = a(x - h)^2 + k[/tex]
[tex]6 = a(-5 - (-3))^2 - 2[/tex]
[tex]6 = a(-2)^2 - 2[/tex]
[tex]6 = 4a - 2[/tex]
Solve for a
[tex]4a = 6 + 2[/tex]
[tex]4a = 8[/tex]
[tex]a = 2[/tex]
So:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = 2(x - (-3))^2 -2[/tex]
[tex]y = 2(x +3)^2 -2[/tex]