The equation of the parabola is [tex]\mathbf{y =-\frac 49(x - 3)^2 + 5}[/tex]; see attachment for its graph
The given parameters are:
(h,k) = (3,5) --- The vertex
(x,y) = (0,1) ---- the y-intercept
A parabola is represented as:
[tex]\mathbf{y =a(x - h)^2 + k}[/tex]
Substitute the given values in the equation
[tex]\mathbf{1 =a(0 - 3)^2 + 5}[/tex]
Evaluate the bracket
[tex]\mathbf{1 =a(-3)^2 + 5}[/tex]
Expand the bracket
[tex]\mathbf{1 =9a+ 5}[/tex]
Subtract 5 from both sides
[tex]\mathbf-{4 =9a}[/tex]
Divide both sides by 9
[tex]\mathbf{a =- \frac 49}[/tex]
So, the equation of the parabola becomes
[tex]\mathbf{y =a(x - h)^2 + k}[/tex]
[tex]\mathbf{y =-\frac 49(x - 3)^2 + 5}[/tex]
See attachment for the graph of the parabola
Read more about parabolas at:
https://brainly.com/question/21685473
