4a)++Graphing+Quadratic+Functions+in+Standard+and+Vertex+Form

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut34_quadfun.htm Graphing Quadratic Functions in Vertex and Standard Form

Graphing a function in Standard Form Example of Standard Form Function: f(x)= x^2 -4x +5 a= 1 b= -4 c= 5

xv= xv= = 2

yv= x^2 -4x +5 yv= 2^2 -4(2) +5 yv= 4 -8 +5 yv= 1

vertex is at (2,1)

To graph the function you have to make a table of the corresponding x and y values

f(x)= x^2 -4x +5 f(0)= 0^2 -4(0) +5 f(0)= 5

So when x=0, y=5 Your table should look like...

x | y 0 | 5 1 | 2 2 | 1 3 | 2 4 | 5

Graph these points on the graph to graph the function. Remember that if a>0 the function will be graphed upward like a smile(U). If a<0 the function will be graphed downward like a frown. Connect all the points to complete the graphing

Example of a graph where a>0 a=1, faces upward

Example of a graph where a<0 a=-1, graph faces downward

Graphing a function in Vertex Form Example of what a function in vertex form looks like... y= (x-h)^2 +k The vertex is as (h,k)

Example... y= (x+2)^2 +3 The vertex is at (2,3)

Find the x and y points of the function the same way you did for Standard Form functions.

y= (1+2)^2 +3 y= (3)^2 +3 y= 9 +3 y= 12

So when x= 1, y= 12 So far your table should look like... x | y 1 | 11 2 | 3

Continue to plug in x values into the function to find out the corresponding y values. Graph the same way you graphed the function in Standard Form.