Solving Quadratics

1
Solving Quadratics

• By Graphing

2
Vocab review
Do you remember from unit 1?

• Zeros the place where the graph crosses the
  x-axis
• A.K.A x-intercepts or Roots or solutions

Zeros
3
How many solutions does a Quadratic have?

• Sometimes is may have less than 2 solutions.
  Lets see what that looks like.

Two solutions because the highest exponent is 2
4
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
5
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
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Your turn!

• How many solutions do each of these graphs have?
• 1. 2. 3.

1 solution
2 solutions
2 solutions
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Identifying the solutions from the graph
X -2, 2
X -3
X -4, 1
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You try!

• Identify the solutions from the graph

X -2, 2
No solution
X 0
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Writing the equation from the graph.

• Using the solutions from 2 slides ago

X -2, 2
X -3
X -4, 1
Y (x 3)2
Y -(x 4)(x 1)
Y (x 2)(x 2)
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You try!

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

Y - (x 4)2
Y (x 4)(x 1)
Y (x 5)(x 3)
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Finding the solutions from a table
Ex 1
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
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Finding the soln from a table cont.
Ex 2
x -2 -1 0 1 2 3
Y 3 0 -1 0 3 8
Find the solutions.
X -1 and 1
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Finding the soln from a table cont.
Ex 3
x -2 -1 0 1 2 3
Y 16 9 4 1 0 1
Find the solutions.
This problem only has one solution
X 2
Ex 4
x -2 -1 0 1 2 3
Y 6 3 2 3 6 11
This problem no solution
14
Finding the soln from a table cont.
Ex 5
x -2 -1 0 1 2 3
Y 12 5 0 -3 -4 -3
Find the solutions.
This problem has two solution but only one is
listed on the table
X 0 , 4
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Solutions from a table cont.
Ex 6

• 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