Graphs !!!

Standard form of a quadratic equation.

y  =  x² + bx + c

Standard form of a parabolic equation.



y  =  a(x - h)²  + k

vertex (h, k)

• 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 ( ) that moves the parabola to the right or left.
  • you have to move it in the opposite direction.

 

• 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 ( ) that moves the parabola up or down.

 

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