Answer:
[tex]x=1(y-3)^2-5[/tex]
Step-by-step explanation:
we need to find the equation of the parabola with vertex (-5,3), with axis parallel to the x-axis.
general equation of horizontal parabola is
[tex]x=a(y-k)^2+h[/tex]
where (h,k) is the vertex
(-5,3) is the vertex. h=-5 and k=3. plug in the values in the general equation
[tex]x=a(y-3)^2-5[/tex]
Now find out the value of 'a' using x intercept (4,0)
[tex]4=a(0-3)^2-5[/tex]
[tex]4=a(-3)^2-5[/tex]
[tex]4=9a-5[/tex]
Add 5 on both sides
[tex]9=9a[/tex]
a=1
the equation becomes
[tex]x=1(y-3)^2-5[/tex]
