Answer:
[tex]f(x) = - 2( {x - 3)}^{2} + 8[/tex]
Step-by-step explanation:
The quadratic function in the vertex form is:
[tex]f(x) = a( {x - h)}^{2} + k[/tex]
From the given information, k=8 and h is the midpoint of 1 and 5 which is 3
[tex]f(x) = a( {x - 3)}^{2} + 8[/tex]
f(1)=0
[tex]0 = a( {1 - 3)}^{2} + 8[/tex]
[tex] - 8 = 4a[/tex]
[tex]a = - 2[/tex]
The required equation is
[tex]f(x) = - 2( {x - 3)}^{2} + 8[/tex]
