Basic quadratic equation

#Basic-quadratic-equation

The square (x^2) makes it quadratic. Reference graphing quadratic equations tutorial

  • The visual shape is known as a parabola

Transformations

#Transformations

Adding and subtracting on the Y Axis

#Adding-and-subtracting-on-the-Y-Axis

Example 1: Add 10

#Example-1:-Add-10

This example simply adds 10 to the y axis. f(x) = x^2 + 10

  • Notice where the plot bottom is

Example 2: Subtract 10

#Example-2:-Subtract-10

This example takes away 10 to the y axis. f(x) = x^2 - 10

  • Note the bottom is below 0 (-10 below)

Adding and subtracting on the X axis

#Adding-and-subtracting-on-the-X-axis

Example 3: Negative 10

#Example-3:-Negative-10

This example subtracts 10 inside the parenthesis f(x) = (x-10)^2

  • Notice the negative 10 equates to plus 10 on the x axis

Example 4: Positive 10

#Example-4:-Positive-10

This example adds 10 inside the parenthesis f(x) = (x+10)^2

  • Notice the negative 10 equates to plus 10 on the x axis

Flipping the parabola

#Flipping-the-parabola

Example 5: x axis from the previous example

#Example-5:-x-axis-from-the-previous-example

Adding a negative outside the parens flips it. Everything else stays the same

Example 6: y axis from the first example

#Example-6:-y-axis-from-the-first-example

Remember the very first example. Adding a negative outside the parens flips it. Everything else stays the same

Negative inside the parens

#Negative-inside-the-parens

A negative value inside the parens doesn't flip the parabola, but it flips the x axis movement

  • Normally a negative correlates to a positive, but in this case a negative is a negative. Compare example 3 and example 7

Example 7: Negative inside parens

#Example-7:-Negative-inside-parens