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GRAPH QUADRATIC
FUNCTIONS IN VERTEX
FORM
What is Vertex form?
4.2
Graph y = -1/3(x + 3)2 + 7
Graph y = (x + 2)2 - 3
• Identify the vertex
• Identify the vertex
• (-3, 7)
• (-2, -3)
• Draw line of
• Draw line of
Symmetry
• Find another point
•X = 0
• y = -1/3(0+3)2 + 7
• y = -1/3(9) + 7
• y = -3+7 = 4
• (0, 4)
Symmetry
• Find another point
•X = 0
• y = (0+ 2)2 - 3
•y = 4 – 3 = 1
• (0, 1)
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What is intercept form?
Graph y = (x – 3)(x – 7)
• Find the intercepts
• x – 3 = 0, x – 7 = 0
• X = 3, x = 7
• Find the Vertex
5
•
• y = (5 – 3)(5 – 7)
• Y = 2(-2) = -4
• The path of a placekicked football can be modeled by the
Graph y = 2(x – 2)(x + 1)
• Find the intercepts
• x – 2 = 0, x + 1= 0
• X = 2, x = -1
• Find the Vertex
0.5
•
• y=2(0.5– 2)(0.5+1)
• Y = 2(-1.5)(1.5)
= -4.5
function y = -0.025x(x – 50) where x is the horizontal distance
(in yards) and y is the corresponding height (in yards).
• How far is the football kicked?
• This is found by finding the intercepts.
•
y = -0.025(x – 0)(x – 50)
• 100
x–0=0
x – 50 = 0
• 90
x=0
x = 50
• 80
What is the maximum height?
70
•
Find the vertex.
60
25
• 50
y = -0.025(25)(25 – 50)
y = -0.025(-625) = 15.625
Maximum height of 15.625
• 40
• 30
•
20
10
0 10 20 30 40 50 60 70 80 90 100
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Changing to different forms
Change from vertex to standard
• To change from intercept form to standard form, you will
• Use FOIL or the Box method.
use FOIL or the box method.
• y = 2(x + 2)(x – 5)
• y = 2(x2 -5x + 2x – 10)
•y=
x
x
x2
+2
2x
2x2
– 10x + 4x – 20
• y = 2x2 – 6x - 20
• y = 2(x -1)2 – 5
x
-1
x
x2
-x
-1
-x
1
• y = 2(x – 1)(x – 1) – 5
•y=
2(x2
– x – x +1) - 5
• y = 2x2 – 2x – 2x +2 – 5
• y = 2x2 – 4x – 3
-5
-5x
-10
2(X2-3x-10)
2x2 – 6x - 20
2(X2-2x+1)-5
2x2 – 4x +2 – 5 = 2x2 – 4x – 3
3