Do the points (−1,9) and (2,4) represent the vertex and a sample point, respectively, of y=−2(x+1)2+9? Explain

Vertex: (-1,9) is true

Sample Points: (2,4) is not true

Step-by-step explanation:

Given

Required

Determine if the vertex and sample points exist for

Solving for the vertex:

Writing the given equation in the form:

Expand the bracket

Open Bracket

Open bracket

Solve for x using:

Where ;

So:

Substitute -1 for x in

Simplify all brackets

Hence;

The vertex (x,y) is (-1,9)

This is true

Checking sample points:

In this case; and

Substitute and in

Hence;

This sample points does not exist

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step-by-step explanation:

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