Mathematics: Which inequality does the graph below represent?

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Which inequality does the graph below represent?

eaves001

10.03.2022

A. $y\le2x^2-8x+3$

Step-by-step explanation:

The given parabola has vertex at (2,-5).

The equation of this parabola in vertex form is given by:

y=a(x-h)^2+k , where (h,k)=(2,-5) is the vertex of the parabola.

We substitute the values to get:

y=a(x-2)^2-5

The graph passes through; (0,3).

3=a(0-2)^2-5

$\implies 3+5=4a$

$\implies 8=4a$

$\implies a=2$

Hence the equation of the parabola is

y=2(x-2)^2-5

We expand this to get:

y=2x^2-8x+8-5

y=2x^2-8x+3

Since the outward region was shaded, the corresponding inequality is

$y\le2x^2-8x+3$

The correct answer is A

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