Transcript Unit 5 Part 2 Factoring and Solving Quadratic Equations

GRAPHING QUADRATIC FUNCTIONS
VERTEX FORM
Goal: I can complete the square in a quadratic expression to
reveal the maximum or minimum value.
(A-SSE.3b)
VOCABULARY:
Parabola-
The U-shaped graph of a quadratic function
Vertex-
The highest (maximum) or lowest (minimum) point on a
parabola
Axis of symmetryThe vertical line that passes through the vertex and divides
the parabola into 2 equal parts
VERTEX FORM OF A QUADRATIC
FUNCTION
Given the function y = a(x – h)2 + k
If a > 0, the parabola opens up
If a < 0, the parabola opens down
The axis of symmetry is x = h
The vertex is (h, k)
VERTEX FORM OF A QUADRATIC
FUNCTION
EXAMPLE
y   x  3  2
2
Determine the a to decide if the parabola opens up or
down or it’s a minimum or maximum, the coordinates of
the vertex and the line of symmetry.
a: 1
Opens : Up
Now let’s Graph!
Minimum
Vertex :  3, 2 
Line of Symmetry : x  3
Now let’s Graph!
EXAMPLE y   x  3  2
2
FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
3. Plot points:
2. Make a table of values:
y = (-5 +3)2 + 2
y = (-4
+3)2
+2
X
-5
-4
Y
6
3
vtx
y = (-2 +3)2 + 2
y = (-1
+3)2
+2
-3
2
-2
3
-1
6
EXAMPLE y   x  2   6
2
Determine the a to decide if the parabola opens up or
down or it’s a minimum or maximum, the coordinates of
the vertex and the line of symmetry.
a: 1
Opens : Up
Now let’s Graph!
Minimum
Vertex :  2, 6 
Line of Symmetry : x  2
Now let’s Graph!
EXAMPLE y   x  2   6
2
FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
3. Plot points:
2. Make a table of values:
y = (-4 +2)2 - 6
y = (-3
+2)2
-6
X
-4
-3
Y
-2
-5
vtx
y = (-1 +2)2 - 6
y = (0
+2)2
-6
-2
-6
-1
-5
0
-2
EXAMPLE
y  4  x  3 
2
Determine the a to decide if the parabola opens up or
down or it’s a minimum or maximum, the coordinates of
the vertex and the line of symmetry.
a : 4
Opens : Down
Now let’s Graph!
Maximum
Vertex :  3, 0 
Line of Symmetry : x  3
Now let’s Graph!
EXAMPLE y  4  x  3
2
FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
3. Plot points:
2. Make a table of values:
y = -4(1 -3)2
y = -4(2
-3)2
X
1
2
Y
-16
-4
vtx
y = -4(4 -3)2
y = -4(5
-3)2
3
0
4
-4
5
-16
CHANGE A QUADRATIC FUNCTION FROM
STANDARD FORM TO VERTEX FORM
 Move the constant
 Add (b/2)2 to each side
 Factor the perfect square trinomial
y  x2  4x  6
2
y  6  x  4x
y  6  4  x2  4x  4
y  2   x  2
2
y   x  2  2
2
 Write in the form y = a(x – h)2 + k
Now let’s Graph!
Now let’s Graph!
EXAMPLE y   x  2   2
2
FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
3. Plot points:
2. Make a table of values:
y = (-4 +2)2 + 2
y = (-3
+2)2
+2
X
-4
-3
Y
6
3
vtx
y = (-1 +2)2 + 2
y = (0
+2)2
+2
-2
2
-1
3
0
6
WRITE THE QUADRATIC IN VERTEX FORM
y  x2  4x 1
2
y 1  x  4x
y  1  4  x2  4x  4
 Move the constant
 Add (b/2)2 to each side
 Factor the perfect square trinomial
 Write in the form y = a(x –
h)2
+k
y  5   x  2
2
y   x  2  5
2
Now let’s Graph!
Now let’s Graph!
EXAMPLE
y   x  2  5
2
FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
3. Plot points:
2. Make a table of values:
y = (0 -2)2 - 5
y = (1
-2)2
-5
X
Y
0
-1
-4
1
vtx
y = (3 -2)2 - 5
y = (4
-2)2
-5
2
-5
3
-4
4
-1