Answer :
Answer:
[tex]y=-2(x+5)^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 given vertex is (-5,-3), thus:
[tex]y=a(x-(-5))^2-3[/tex]
[tex]y=a(x+5)^2-3[/tex]
We need to find the value of a. We use the point (-4,-5):
[tex]-5=a(-4+5)^2-3[/tex]
[tex]-5=a(1)^2-3[/tex]
[tex]-5=a-3[/tex]
Solving:
[tex]a=-5+3=-2[/tex]
The complete equation of the parabola is:
[tex]\mathbf{y=-2(x+5)^2-3}[/tex]