graphing quadratic functions vertex form goal: i can complete the square in a quadratic expression...
TRANSCRIPT
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-
Vertex-
Axis of symmetry-
The U-shaped graph of a quadratic function
The highest (maximum) or lowest (minimum) point on a parabola
The 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 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.
23 2y x
3x 3,2
:a 1
:Opens Up
Minimum
:Vertex
:Line of Symmetry
Now let’s Graph!
2. Make a table of values:
EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
X Y
vtx
-2
-5-4-3
-1
y = (-5 +3)2 + 26
3
2
3
6
y = (-4 +3)2 + 2
y = (-2 +3)2 + 2y = (-1 +3)2 + 2
23 2y x
Now let’s Graph!
3. Plot points:
EXAMPLE 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.
2x 2, 6
:a 1
:Opens Up
Minimum
:Vertex
:Line of Symmetry
Now let’s Graph!
22 6y x
2. Make a table of values:
EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
X Y
vtx
-1
-4-3-2
0
y = (-4 +2)2 - 6-2
-5
-6
-5
-2
y = (-3 +2)2 - 6
y = (-1 +2)2 - 6y = (0 +2)2 - 6
Now let’s Graph!
3. Plot points:
22 6y x
EXAMPLE 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.
3x 3,0
:a 4:Opens Down
Maximum
:Vertex
:Line of Symmetry
Now let’s Graph!
24 3y x
2. Make a table of values:
EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
X Y
vtx
4
1
23
5
y = -4(1 -3)2
-16
-4
0
-4
-16
y = -4(2 -3)2
y = -4(4 -3)2
y = -4(5 -3)2
Now let’s Graph!
3. Plot points:
24 3y x
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
Write in the form y = a(x – h)2 + k
2 4 6y x x 26 4y x x 26 4 4 4y x x
22 2y x
22 2y x
Now let’s Graph!
2. Make a table of values:
EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
X Y
vtx
-1
-4-3-2
0
y = (-4 +2)2 + 26
3
2
3
6
y = (-3 +2)2 + 2
y = (-1 +2)2 + 2y = (0 +2)2 + 2
Now let’s Graph!
3. Plot points:
22 2y x
WRITE THE QUADRATIC IN VERTEX FORM
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
2 4 1y x x 21 4y x x 21 4 4 4y x x
25 2y x
22 5y x
Now let’s Graph!
2. Make a table of values:
EXAMPLE FILL IN THE TABLE OF VALUES TO GRAPH THE QUADRATIC.
X Y
vtx
3
0
1
2
4
y = (0 -2)2 - 5-1
-4
-5
-4
-1
y = (1 -2)2 - 5
y = (3 -2)2 - 5
y = (4 -2)2 - 5
Now let’s Graph!
3. Plot points:
22 5y x