Step-by-step explanation:
[tex]y = a {(x - h)}^{2} + k[/tex]
[tex]vertex = (h \: \: \: k)[/tex]
from the table
[tex]vertex = ( - 2 \: \: \: 4)[/tex]
therefore
[tex]h = - 2 \: \: and \: \: k = 4[/tex]
[tex]y = a {(x + 2)}^{2} + 4[/tex]
when x= 0, y = 3
[tex]3 = a {(2)}^{2} + 4[/tex]
[tex]3 = 4a + 4[/tex]
[tex]a = \frac{ - 1}{4} [/tex]
therefore equation of the function
[tex]y = - \frac{1}{4} {(x + 2)}^{2} + 4[/tex]
