y = [tex]\frac{1}{2}[/tex](x + 6)² + 4
the equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (- 6, 4 ), hence
y = a(x + 6 )² + 4
To find a substitute (- 2, 12) into the equation
12 = 16a + 4 ( subtract 4 from both sides )
8 = 16a ( divide both sides by 16 )
a = [tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex](x + 6 )² + 4 ← in vertex form
