Warm Up 5-5
Simplify the Radical.
1) 5
32
4
Complete the square.
5) 𝑥 2 + 18𝑥 + 56
Solve equations using the square root.
2)
=0
25
3
3)
𝑥 2 = −11
4) 2𝑥
2
− 54 = 0
Solve equations using the zero product.
6) 𝑥 2 − 11𝑥 + 18 = 0
Solve equation using the zero product.
7) 𝑥 2 +𝑥 = 4
Unit 8 Day 7: Graphing
Quadratic Equations
Essential Question: How do we graph
a quadratic function?
1) Function: y = x2 – 3x + 2
a =1
b = -3
c=2
Leading Coefficient: The graph opens:
a=
• up
(circle one)
1
• down
Discriminant:
(-3)2 - 4(1)(2)
9-8
1
Quadratic Formula:
How many solutions does the equation
have? (circle one)
• TWO
• ONE
• NO REAL SOLUTIONS
Find the solutions by using the
quadratic formula/factoring.
(x - 2)(x - 1) = 0
OR factor if you can!
x-2=0
x-1=0
x=2
x=1
Quadratic Formula:
Find the solutions by using the
quadratic formula.
2&1
Vertex:
3
x=
= 3/2
2(1)
x
Table of Values:
y = x2 – 3x + 2
0
(0)2 - 3(0) + 2 = 0 - 0 + 2
=2
2
1
(1)2 - 3(1) + 2
=0
0
vertex:
3/2
=1-3 +2
y
(3/2)2 - 3(3/2) + 2 = 9/4 - 9/2 + 2 = -1/4 -1/4
2
(2)2 - 3(2) + 2
=4-6 +2
=0
0
3
(3)2 - 3(3) + 2
= 9- 9 + 2
=2
2
The Graph!
Now use all the
information you
found to graph
the parabola.
x
y
0
1
3/2
2
3
2
0
-1/4
0
2
Graph:
1. The vertex
(and how it opens).
2. The x-intercepts
(where it crosses the x-axis).
3. The (x , y) values
from the table.
4. Connect the dots!
10
5
-10
-5
5
You can do it!
-5
-10
10
2) Function: y = -2x2 + 6x - 3
a = -2
b= 6
c = -3
Leading Coefficient: The graph opens:
a=
• up
(circle one)
-2
• down
Discriminant:
(6)2 - 4(-2)(-3)
36 - 24
12
Quadratic Formula:
OR factor if you can!
How many solutions does the equation
have? (circle one)
• TWO
• ONE
• NO REAL SOLUTIONS
Find the solutions by using the
quadratic formula/factoring.
x=
-6 ± 12
2 (-2)
=
-3 + 3
-2
-6 ± 2 3
-4
-3 -
3
-2
Quadratic Formula:
Find the solutions by using the
quadratic formula.
-3 + 3
-2
Vertex:
-6
x=
= 3/2
2(-2)
&
-3 -
3
-2
x
Table of Values:
y = -2x2 + 6x - 3
y
0
-2(0)2 + 6(0) - 3
-3
1
-2(1)2 + 6(1) - 3
1
3/2
-2(3/2)2 + 6(3/2) - 3
3/2
2
-2(2)2 + 6(2) - 3
1
3
-2(3)2 + 6(3) - 3
-3
vertex:
The Graph!
Now use all the
information you
found to graph
the parabola.
x
y
0
1
3/2
2
3
-3
1
3/2
1
-3
Graph:
1. The vertex
(and how it opens).
2. The x-intercepts
(where it crosses the x-axis).
3. The (x , y) values
from the table.
4. Connect the dots!
10
5
-10
-5
5
You can do it!
-5
-10
10
3) Function: y = x2 - 8x + 16
a= 1
b = -8
c = 16
Leading Coefficient: The graph opens:
a=
• up
(circle one)
1
• down
Discriminant:
(-8)2 - 4(1)(16)
64 - 64
0
Quadratic Formula:
How many solutions does the equation
have? (circle one)
• TWO
• ONE
• NO REAL SOLUTIONS
Find the solutions by using the
quadratic formula/factoring.
(x - 4)(x - 4) = 0
OR factor if you can!
x-4=0
x=4
Quadratic Formula:
Find the solutions by using the
quadratic formula.
4
Vertex:
8
x=
=4
2(1)
x
Table of Values:
y = x2 – 8x + 16
y
2
(2)2 - 8(2) + 16
4
3
(3)2 - 8(3) + 16
1
4
(4)2 - 8(4) + 16
0
5
(5)2 - 8(5) + 16
1
6
(6)2 - 8(6) + 16
4
vertex:
The Graph!
Now use all the
information you
found to graph
the parabola.
x
y
2
3
4
5
6
4
1
0
1
4
Graph:
1. The vertex
(and how it opens).
2. The x-intercepts
(where it crosses the x-axis).
3. The (x , y) values
from the table.
4. Connect the dots!
10
5
-10
-5
5
You can do it!
-5
-10
10
4) Function: y = x2 - x + 1
a= 1
b = -1
c=1
Leading Coefficient: The graph opens:
a=
• up
(circle one)
1
• down
Discriminant:
(-1)2 - 4(1)(1)
1-4
-3
Quadratic Formula:
OR factor if you can!
How many solutions does the equation
have? (circle one)
• TWO
• ONE
• NO REAL SOLUTIONS
Find the solutions by using the
quadratic formula/factoring.
We don’t need to
use this because
there are no
solutions!
Quadratic Formula:
Find the solutions by using the
quadratic formula.
NRS
Vertex:
1
x=
= 1/2
2(1)
x
Table of Values:
y = x2 – x + 1
y
-1
(-1)2 - (-1) + 1
3
0
(0)2 - (0) + 1
1
1/2
(1/2)2 - (1/2) + 1
3/4
1
(1)2 - (1) + 1
1
2
(2)2 - (2) + 1
3
vertex:
The Graph!
Now use all the
information you
found to graph
the parabola.
x
y
-1
0
1/2
1
2
3
1
3/4
1
3
Graph:
1. The vertex
(and how it opens).
2. The x-intercepts
(where it crosses the x-axis).
3. The (x , y) values
from the table.
4. Connect the dots!
10
5
-10
-5
5
You can do it!
-5
-10
10
Summary
Respond to the essential question in the
summary potion of your notes.
Essential Question: How do we graph
a quadratic function?