6.6 Analyzing Graphs of Quadratic Functions

6.6 Analyzing Graphs of Quadratic Functions Write a Quadratic Equation in Vertex form

Vertex form of the Quadratic Equation So far the only way we seen the Quadratic Equation is ax2 + bx + c =0. This form works great for the Quadratic Equation. Vertex form works best for Graphing. We need to remember how to find the vertex. The x part of the vertex come from part of the quadratic equation.

Vertex form of the Quadratic Equation The x part of the vertex come from part of the quadratic equation. To find the y part, we put the x part of the vertex. The vertex as not (x, y), but (h, k)

Find the vertex of the Quadratic Equation

The Vertex form of the Quadratic Equation

Write the Quadratic Equation in Vertex form Find a, h and k a= 1 h = -1 k = 3

Vertex is better to use in graphing y = 2(x - 3)2 – 2 Vertex (3 , -2) Put in 4 for x, y = 2(3 - 4)2 – 2 (4, 0) Then (2, 0) is also a point

Let see what changes happen when you change “a”

Let see what changes happen when you change “a” The larger the “a”, the skinner the graph What if “a” is a fraction?

Let see what changes happen when you change “a” What if “a” is a fraction?

What if we change “h” in the Vertex Let a = 1, k = 0 Changing the “h” moves the graph Left or Right.

What if we change “k” in the Vertex Let a = 1, h = 0 “k” moves the graph up or down.

Write an equation Given the vertex and a point on the graph. The vertex gives you “h” and “k”. We have to solve for “a” Given vertex (1, 2) and point on the graph passing through (3, 4) h =1; k = 2

Write an equation Given vertex (1, 2) and point on the graph passing through (3, 4) x=3, y=4 Solve for “a”

Write an equation a = ½ Solve for “a”

Write an equation a = ½ Final Answer

Homework Page 326 – 327 # 15 – 25 odd, 27, 31, 39 – 45 odd

Homework Page 326 – 327 # 16 – 26 even, 28, 32, 40 – 46 even

6.6 Analyzing Graphs of Quadratic Functions