7 January 2011 Algebra 2. Solving Quadratics by Graphing 1/7 Using a Graph To solve a quadratic equation with a graph, look for the points where the graph

7 January 2011

Algebra 2

Solving Quadratics by Graphing 1/7Using a

GraphTo solve a quadratic equation with a graph, look for the points where the graph crosses the x-axis



x-axis



x-axis

crosses here and here



x-axis

crosses here and here solutions: (-1,0) and (4,0)


GraphFind the solutions to the function f(x)=x2 – x – 6



x-axis




x-axis


Solutions: (-2,0) and (3,0)

What are the solutions to the function f(x) = x² – 3x – 10

1. (0,2) and (0,5)2. (0,2) and (0,-5)3. (0,-2) and (0,5)4. (2,0) and (5,0)5. (-2,0) and (5,0)

What are the solutions to the function f(x) = x2 – 6x + 9

1. (0,2)2. (0,3)3. (2,0)4. (3,0)

What are the solutions to the function f(x) = x2 – 6x + 10

1. (0,0)2. (0,3)3. No Solution4. (3,0)

Solving Quadratics by Graphing 1/7By

GraphingMake your own graph, then see where it crosses the x-axis.

f(x) = x2 – 6x + 5

1.Find the vertex using 2.Create a table3.Add to the table until you get a 0 for y4.Graph the points you found

a

b

2


Graphingf(x) = x2 – 6x + 5

1.Find the vertex using

b = -6 a = 1

a

b

2




b = -6 a = 1

= =

a

b

2

a

b

2

)1(2

)6(




b = -6 a = 1

= = = 3

a

b

2

a

b

2

)1(2

)6(2

6




b = -6 a = 1

= = = 3

(3)2 – 6(3) + 5 = -4

a

b

2

a

b

2

)1(2

)6(2

6




b = -6 a = 1

= = = 3

(3)2 – 6(3) + 5 = -4 vertex = (3,-4)

a

b

2

a

b

2

)1(2

)6(2

6



1.Find the vertex : (3,-4)2.Create a table

Start with your vertex

3

-4




Go out by 1 until you get a 0 for y

3 4

-4 -3




Go out by 1 until you get a 0 for yStop.

3 4 5

-4 -3 0




Fill in the other side of the table an equal number of places

1 2 3 4 5

0 -3 -4 -3 0


Graphing4. Graph the points you found

Solutions: (1,0) and (5,0)

Documents

7 January 2011 Algebra 2. Solving Quadratics by Graphing 1/7 Using a Graph To solve a quadratic equation with a graph, look for the points where the graph