Which of these functions best describes this graph?

The correct option is A.

Step-by-step explanation:

The vertex from of a parabola is

Where, (h,k) is vertex of the parabola and a is a Constant.

From the given graph it is clear that the vertex of the parabola is (1,0) and the y-intercept is (0,1).

The vertex of the parabola is (1,0). Put h=1 and k=0 in the above equation.

          ... (1)

The graph passing through (0,1).

Put a=1 in equation (1) to find the equation of parabola is

Therefore option A is correct.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

stethere all not eveanp-by-step explanation: