Answer:
A. [tex]y\le2x^2-8x+3[/tex]
Step-by-step explanation:
The given parabola has vertex at (2,-5).
The equation of this parabola in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex], where (h,k)=(2,-5) is the vertex of the parabola.
We substitute the values to get:
[tex]y=a(x-2)^2-5[/tex]
The graph passes through; (0,3).
[tex]3=a(0-2)^2-5[/tex]
[tex]\implies 3+5=4a[/tex]
[tex]\implies 8=4a[/tex]
[tex]\implies a=2[/tex]
Hence the equation of the parabola is
[tex]y=2(x-2)^2-5[/tex]
We expand this to get:
[tex]y=2x^2-8x+8-5[/tex]
[tex]y=2x^2-8x+3[/tex]
Since the outward region was shaded, the corresponding inequality is
[tex]y\le2x^2-8x+3[/tex]
The correct answer is A
