Answer:
[tex]y=-(x-2)^2-3[/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 that results when plotting the function, and a is a coefficient different from zero.
The graph provided in the question has two clear points:
The vertex, located at (2,-3)
The y-intercept, located at (0,-7)
Substituting the coordinates of the vertex, the equation of the function is:
[tex]y=a(x-2)^2-3[/tex]
The value of a will be determined by using the other point:
[tex]-7=a(0-2)^2-3[/tex]
Operating:
[tex]-7=a(4)-3[/tex]
[tex]4a=-4\Rightarrow a=-4/4[/tex]
Solving:
a=-1
The equation of the graph is:
[tex]y=-(x-2)^2-3[/tex]
