Question

In two or more complete sentences, describe how you would draw the graph of the solution set for the following inequality.

-3m+18 < 30

Answer 1

Explanation:

A nonlinear function that can be written on the standard form

ax2+bx+c,wherea≠0ax2+bx+c,wherea≠0

is called a quadratic function.

All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is

y=x2y=x2

The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate

x=−b2ax=−b2a

The y-coordinate of the vertex is the maximum or minimum value of the function.

a > 0 parabola opens up minimum value

a < 0 parabola opens down maximum value

A rule of thumb reminds us that when we have a positive symbol before x2we get a happy expression on the graph and a negative symbol renders a sad expression.

The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equation

x=−b2ax=−b2a

The y-intercept of the equation is c.

When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.

Answer 2

`m>-4` is the solution set.

Explanation:

To graph the solution set of the given inequality:

• First, we need to graph the expression as an equality:
  `-3m+18=30`.
• Then, we must evalue a test point (0,0), to know which area is solution, the upper area or the lower area.
• Finally, we ensure that the line is non solid, because the inequality sign doesn't include a relation of equivalence.

The image attached shows the area of solution to the give inequality.