Equation :
This parabola is facing downwards and highest point of the parabola is it's vertex.
Highest point is (-2,2)
so the vertex is (-2,2)
The graph is passing through (-1,0)
Equation in vertex form is
[tex]y = a(x - h) {}^{2} + k[/tex]
[tex]0 = a( - 1 + 2) {}^{2} + 2 \\ 0 =a (1) {}^{2} +2 \\ 0 = a + 2 \\ a = - 2 [/tex]
Substitute back in Equation
[tex]y = - 2(x + 2) {}^{2} + 2[/tex]
the graph has two x intercepts -1 and -3
that means (x+1) and (x+3) are the factors
multiply factors to get the equation in standard form
[tex]-2(x + 1)(x + 3) = 0 \\ -2(x {}^{2} + x + 3x + 3) = 0 \\ -2( x {}^{2} + 4x + 3) = 0[/tex]
-2x^2-8x-6=0
