Parabolas

Parabolas can be graphed in 2 different ways. The standard form of the equation is:

a, b, and c can be any real number, but we usually use integers (...-1, 0, 1...).

Find the vertex with:

Example

Since a parabola is symmetric, if we find one more point we can graph it... So, plug in x=0 because it is the easiest number:

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12 Main Functions with Domain and Range

A quick explanation on domain and range... Domain is just where the graph has points on the x-axis and range is where the graph has values on the y-axis. R means all real numbers and Z means integers, or ...-1,0,1... If you are a student in Algebra just memorize this ASAP, you will thank me. Haha.

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12 Main Function Transformations

Graphing becomes easier once you understand how transformations work.

• x-shifts go left and right (x-axis) opposite the sign in the equation, so if it is negative you shift right and positive you shift left. y-shifts go up and down (y-axis) the same direction of the sign, positive is an up shift and negative is a down shift.
• If the front of the equation is negative, then you flip your graph up-side down (over the x-axis). If the x is negative, then you flip it horizontally (over the y-axis).
• There is a stretch if you multiply the front of the equation by a number bigger than 1, but it becomes wider if you multiply it by a fraction smaller than 1.
  Some examples:

Example 1

List what you need:

• Use # 2 as a reference (the x-squared function)
• x-shift: -2 (left 2)
• y-shift: +3 (up three)
  becomes
  As you can see, the bullet points describe the transformation perfectly!

Example 2

List the transformations:

• Use # 4 as a reference (the square root function)
• A stretch of 3 times
• Since the 3 out front is negative we flip it up-side down
• No x-shift since there is nothing in the square root with the x
• y-shift: -3 (down 3)
  becomes

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Thank you for viewing Steemians! I hope you learned a lot! Just Pre-calculus and Calculus and you are a master of basic graphing! Study and Enjoy!