Answer :
Solution:
Given that a parabola of vertex (-1, -9) and a point (-3, -5)
Where
[tex]y=a(x-h)^2+k[/tex]To find the value of a, we will find the equation of the parabola first
Where
[tex]\begin{gathered} (h,k)=(-1,-9) \\ (x,y)=(-3,-5) \end{gathered}[/tex]Substitute the values of the variable into the formula above
[tex]\begin{gathered} y=a(x-h)+k \\ -5=a(-3-(-1))+(-9) \\ -5=a(-3+1)-9 \\ -5=a(-2)-9 \\ -5=-2a-9 \\ Collect\text{ like terms} \\ -2a=-9+5 \\ -2a=-4 \\ Divide\text{ both sides by -2} \\ \frac{-2a}{-2}=\frac{-4}{-2} \\ a=2 \end{gathered}[/tex]Hence, the value of a is 2
