Answer:
[tex]y=-5(x-4)^2+4[/tex]
Step-by-step explanation:
Equation of the Quadratic Function
The vertex form of the quadratic function has the following equation:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola, and a is a coefficient different from zero.
The vertex is located at (4,4).
Substituting the coordinates of the vertex, the equation of the function is:
[tex]y=a(x-4)^2+4[/tex]
The value of a will be determined by using the given point (3,-1).
[tex]-1=a(3-4)^2+4[/tex]
Operating:
[tex]-1=a(1)+4[/tex]
Solving:
[tex]a=-5[/tex]
The equation of the graph is:
[tex]\boxed{y=-5(x-4)^2+4}[/tex]
