Answer:
[tex]y=-3(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, assumed as a parabola, has two clear points:
The vertex, located at (-2,-3)
The point (-1,-6)
Substituting the coordinates of the vertex, the equation of the function is:
[tex]y=a(x-(-2))^2-3[/tex]
[tex]y=a(x+2)^2-3[/tex]
The value of a will be determined by using the other point (-1,-6):
[tex]-6=a(-1+2)^2-3[/tex]
Operating:
[tex]-6=a(1)-3[/tex]
Solving:
a=-3
The equation of the graph is:
[tex]\boxed{y=-3(x+2)^2-3}[/tex]
