Graphing Quadratic Equations

The standard form of a quadratic equation is:

y  =  x² + bx + c

The standard form of a parabolic equation is:



y  =  a(x - h)²  + k

vertex (h, k)

• Changing a...if you change a, it makes the graph open up or down
• Up when a is positive
• Down when a is negative
• Fractions (0 < a < 1) make the parabola wider
• Numbers (a > 1) make the graph narrower

• Changing h...h is the number inside the parenthesis that moves the parabola to the right or left
• you have to move it in the opposite direction

So

• if you have (x + 2)² the graph moves two places to the left
• if you have (x - 3)² the graph moves three places to the right

• Changing k...k is the number outside the parenthesis that moves the parabola up or down

So

• if you have (x)² + 2 the graph moves up two places
• if you have (x)² - 3 the graph moves down three places