Answer:
Step-by-step explanation:
This is a parabola with a vertex at h = 4 and k = 5; the graph goes through the coordinate x = 6 and y = 6. We will use those 4 values to fill in the equation:
[tex]y=a(x-h)^2+k[/tex] and this will allow us to solve for the value of a:
[tex]6=a(6-4)^2+5[/tex] and
[tex]6=a(2)^2+5[/tex] and
6 = 4a + 5 and
1 = 4a so
[tex]a=\frac{1}{4}[/tex] and the equation is
[tex]y=\frac{1}{4}(x-4)^2+5[/tex]
