Solving Quadratic EquationsBy Graphing

Vocab review

Zeros – the place where the graph crosses the x-axisA.K.A – x-intercepts or Roots or solutions

Do you remember from unit 1?

Zeros

How many solutions does a Quadratic have?

Sometimes is may have less than 2 solutions. Let’s see what that

looks like.

2 5 4 0x x Two solutions because the highest exponent is 2

How many solutions does a Quadratic have?

2 solutions

The graph crosses the x-axis twice

1 solution

The graph crosses the x-axis once

No solution

The graph never crosses the x-axis

How many solutions does a Quadratic have?

2 solutions

The graph crosses the x-axis twice

1 solution

The graph crosses the x-axis once

No solution

The graph never crosses the x-axis

Your turn!

• How many solutions do each of these graphs have?

1. 2. 3.

1 solution 2 solutions 2 solutions

Identifying the solutions from the graph

X = -3 X = -4, 1 X = -2, 2

You try!

X = -2, 2 No solution X = 0

• Identify the solutions from the graph

Writing the equation from the graph.

X = -3 X = -4, 1 X = -2, 2

• Using the solutions from 2 slides ago

Y = (x + 3)2 Y = -(x + 4)(x – 1) Y = (x – 2)(x + 2)

You try!

Write the equation of each graph.1. 2. 3.

Y = - (x – 4)2Y = (x + 4)(x – 1)Y = (x + 5)(x – 3)

Finding the solutions from a table

x 1 2 3 4 5 6

y -2 -1 0 1 0 -1

This table is of a Quadratic with 2 two solutions

Remember: The solution is also called a zero or x-intercept. Meaning that the y-coordinate of the solution is 0

These are my solutions

X = 5, 3

Ex: 1

Finding the sol’n from a table cont.

x -2 -1 0 1 2 3

Y 3 0 -1 0 3 8Find the solutions.

X = -1 and 1

Ex: 2

Finding the sol’n from a table cont.

x -2 -1 0 1 2 3Y 1

69 4 1 0 1

Find the solutions.

X = 2 This problem only has one solution

x -2 -1 0 1 2 3

Y 6 3 2 3 6 11

This problem no solution

Ex: 3

Ex: 4

Finding the sol’n from a table cont.

x -2 -1 0 1 2 3Y 1

25 0 -3 -4 -3

Find the solutions.

X = 0 , 4This problem has two solution but only one is listed on the table

Ex: 5

There are zeros between -5 and -4 and between 1 and 2

Finding the solutions from a graph

Solutions from a table cont.

Find the interval where the zero is.

x 1 2 3 4 5 6

y 5 1 -2 -7 -3 2

The zeros are between 2 and 3 and between 5 and 6

Ex: 6