ALGEBRA 2 TUTORIAL
Chapter 5 Section 1
Graphing Quadratic Functions
GOAL: Know how to graph a parabola written in vertex form.

The graph of a quadratic function is U-shaped and is called Parabola.
The lowest or highest point on the graph of a quadratic function is called vertex.
The axis of symmetry for the graph of the quadratic function is the vertical line through the vertex.

Quadratic Function : y = ax2 + bx + c

Vertex form is the form of quadratic function.

Vertex Form : y = a ( x - h ) 2 +k the vertex is ( h, k) the axis of symmetry is x = h

Example1 : y = ( x - 1 ) 2 + 2 Step1)) The function is in vertex form y = a ( x - h ) 2 +k Step2)) It has a vertex of ( 1, 2 ) so the axis symmetry is 1 Step3)) ( x - 1 ) 2 gives the standard form equation. ( x - 1 ) 2 -> x2 - 2x + 1 Step4)) Put any numbers in y = ( x - 1 ) 2 + 2 to find the points. y = ( 3 - 1 )2 + 2 y = ( 2 )2 + 2 y = 4 + 2 y = 6 y = (2 - 1 )2 + 2 y = (1 )2 + 2 y =1 + 2 y = 3 y = (0 - 1 )2 + 2 y = (-1 )2 + 2 y =1 + 2 y = 3 y = (-1 - 1 )2 + 2 y = (-2 )2 + 2 y =4 + 2 y = 6 Step5)) Make a table. X Y 3 2 1 0 -1 6 3 2 3 6 Step6)) Graph it.

Example2 : y = -1/2 ( x + 3 )2 -4 Step1)) The function is in vertex form y = a ( x - h ) 2 +k Step2)) It has a vertex of ( -3, -4 ) so the axis symmetry is -3 Step3)) ( x + 3 )2 gives the standard form equation. ( x + 3 )2 -> x2 + 6 x + 9 Step4)) Put any numbers in y = -1/2 ( x + 3 )2 -4 to find the points. y = -1/2 ( -1 + 3 )2 - 4 y = -1/2 ( 2 )2 - 4 y = -1/2 ( 4 ) - 4 y = -2 - 4 y = -6 y = -1/2 ( -2 + 3 )2 - 4 y = -1/2 ( 1 )2 - 4 y = -1/2 ( 1 ) - 4 y = -1/2 - 4 y = -4.5 y = -1/2 ( -4 + 3 )2 - 4 y = -1/2 ( -1 )2 - 4 y = -1/2 ( 1 ) - 4 y = -1/2 - 4 y = -4.5 y = -1/2 ( -5 + 3 )2 - 4 y = -1/2 ( -2 )2 - 4 y = -1/2 ( 4 ) - 4 y = -2 - 4 y = -6 Step5)) Make a table. X Y -1 -2 -3 -4 -5 -6 -4.5 -4 -4.5 -6 Step6)) Graph it. Practice: Graph the quadratic function. Label the vertex and axis of symmetry. a)) y = -2 ( x + 3 )2 -4 b)) y= 5/4 ( x - 3 )2