Graphing Quadratic Functions

• To graph a quadratic function, you need:
  1. vertex (h, k)
  2. direction it opens
• Other information that is helpful in graphing your quadratic function
  1. x-intercepts
• There are two forms that a quadratic function can be in. Each has its own strength/benefit.

y = a(x-h)2 + k	y = ax2 + bx + c
Easy to find the vertex. Just pull out (h, k)	Easy to find x-intercepts. Set y equal to zero and factor or use quadratic formula.
To find x-intercepts you must set y equal to zero and then either: isolate the perfect square that contains the variable and then take the square root of both sides to solve. Foil it out and then factor or use the quadratic formula to solve.	To find the vertex, either complete the square to get it in the form y = a(x-h)2 + k,and now pull out (h, k) Use h = -b/2a to find the x-coordinate of your vertex. Then plug this x value into your function to find the y-coordinate of your vertex, k. Thus: