Answer:
[tex]y = x^2 + 6x + 8[/tex]
Step-by-step explanation:
The equation can be written using information from the graph. The vertex of the parabola is (-3,-1). Use the vertex form [tex]y = a(x-h)^2 + k[/tex] by substituting h = -3 and k = -1. The equation becomes [tex]y = a(x--3)^2 + -1[/tex]. It simplifies to [tex]y = a(x+3)^2 - 1[/tex]. To find a, substitute the point (x,y) on the graph into the equation and solve for a. Substitute x = -2 and y = 0.
[tex]0 = a(-2+3)^2 - 1[/tex]
[tex]0 = a(1)^2 - 1[/tex]
[tex]0 = a - 1[/tex]
[tex]1 = a[/tex]
So the equation is [tex]y = (x+ 3)^2 - 1[/tex]. Convert to standard form by distributing the parenthesis and combining like terms.
[tex]y = (x+ 3)^2 - 1\\y = x^2 + 3x + 3x + 9 - 1\\y = x^2 + 6x + 8[/tex]
