Question

Which quadratic inequality does the graph below represent?​

Answer 1

Answer:

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

Step-by-step explanation:

we know that

The quadratic function of the figure has a vertex at (2,-5) and the y-intercept is the point (0,3)

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

(h,k) is the vertex

a is a coefficient

we have

$(h,k)=(2,-5)$

substitute

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

with the y-intercept find out the value of a

For x=0,y=3

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

$3=4a-5$

$4a=8$

$a=2$

The equation is

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

$y=2(x^2-4x+4)-5$

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

$y=2x^2-8x+3$

Looking at the graph, the solution is the shaded area below the quadratic equation

so

the value of y must be less than or equal to the quadratic function

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