Answer:
First case The coefficient of the squared term is 4
Second case The coefficient of the squared term is 1/16
Step-by-step explanation:
I will analyze two cases
First case (vertical parabola open upward)
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2}+k[/tex]
where
a is the coefficient of the squared term
(h,k) is the vertex
we have
(h,k)=(-5,-2)
substitute
[tex]y=a(x+5)^{2}-2[/tex]
Find the value of a
Remember that
when the x-value is -4, the y-value is 2.
substitute
For x=-4, y=2
[tex]2=a(-4+5)^{2}-2[/tex]
[tex]2=a(1)-2[/tex]
[tex]a=2+2=4[/tex]
the equation is equal to
[tex]y=4(x+5)^{2}-2[/tex]
therefore
The coefficient of the squared term is 4
Second case (horizontal parabola open to the right)
we know that
The equation of a horizontal parabola in vertex form is equal to
[tex]x=a(y-k)^{2}+h[/tex]
where
a is the coefficient of the squared term
(h,k) is the vertex
we have
(h,k)=(-5,-2)
substitute
[tex]x=a(y+2)^{2}-5[/tex]
Find the value of a
Remember that
when the x-value is -4, the y-value is 2.
substitute
For x=-4, y=2
[tex]-4=a(2+2)^{2}-5[/tex]
[tex]-4=a(4)^{2}-5[/tex]
[tex]-4+5=a(16)[/tex]
[tex]a=1/16[/tex]
the equation is equal to
[tex]x=(1/16)(y+2)^{2}-5[/tex]
therefore
The coefficient of the squared term is 1/16
to better understand the problem see the attached figure
