Graphing Various Functions

Types of Graphs:

  • Quadratic
  • Linear
  • Cubic
  • Rational
  • Square Root

Quadratic Functions

Standard Form: ax^2+bx+c

Graphing Quadratics:

When graphing a quadratic, you start with either the quadratic formula or foiling. In the situation below, foiling is used to find the quadratic equation. FOIL stands for First, Outer, Inner, and Last. In the sets (x+2) and (x-5), you would multiply as the Foil acronym directs. (shown below). You end up with the quadratic equation: x^2+3x-10. From here, you can use the quadratic formula to find the x intercepts. The y intercept was already given, (-10).

Correctly graphed quadratic.

Linear Functions

Standard Form: ax(+/-)b

Graphing Linear Functions:

Correctly graphed linear function

Cubic Functions

Standard Form: ax^3+bx^2+cx+d

Graphing Cubic Functions:

Correctly graphed cubic function.

Rational Functions

Standard Form: 1/x

Graphing Rational Functions:

Correctly graphed rational function.

Square Root Functions

Standard form: √b

Graphing Square Root Functions:

Correctly graphed square root function.

Solving a Multi-Step Equation

This is a simple and easy way to show how to solve a multi-step equation.

Using the quadratic formula

Correctly worked quadratic equation using the quadratic formula.

Quadratic Inequalties

x^2 + 2x – 8 < 0

1. Write the problem.

2. Find the zeros. (Factoring)--(x+4)(x-2)=0, --> (x=-4)(x=2)

3. Graph the quadratic using the x-intercepts (x=-4) and (x+2) and the y-intercept (-8).

4. Since the inequality is less than or equal to 0, (which would be the x axis where y is 0) then you would be looking at the joined part of the quadratic.

5. Write the inequality. --> -4</=x</=2

Why yes, those are American Eagle boxers.^

You can also graph this inequality on a number line. Shown in the picture above. The circles will be shaded on the inside because the inequality is "or equal to." The shaded area is between the two points on the line because we are looking at the joined part of the parabola, not the separated sides.

This is a quadratic inequality just like the one above expect you would be looking at the separated part of the graph instead of the joined part. This would change the way your inequality and your number line would look. You inequality now has an "or" in between your two intercepts because the graph runs in opposite directions. The circles would still be shaded in, but instead of shading between the numbers you would shade towards the arrows, to represent the separation.

Interval Notation

Brackets are used for shaded circles, parentheses for open.

With inequalities that look like this: -4</=x</=2, you write them in coordinate form: (-4,2).

The comma in the parentheses stands for the word "through", so you would read the coordinate "Negative four through positive 2.)

If that inequality was < instead of </=, then it would look like this: [-4,2], because that inequality would have shaded circles.

Infinity symbols explained in the video below.

Comment Stream