To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 5 units and 9 units.

The graph of f(x) shifts 5 units right and 9 units down to graph g(x).

Step-by-step explanation:

The general form of the parabola is

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

The parent function is

The vertex of the parabola is (0,0).

The given function is

The vertex of the parabola is (5,-9).

The vertex of the parabola shifts from (0,0) to (5,-9), therefore the graph of f(x) shifts 5 units right and 9 units down to graph g(x).

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is