#### 4.10 Write Quadratic Functions and Models

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4.10 Write Quadratic Functions and Models

4.10 Write Quadratic
Functions and Models
HEY GUYS THIS IS NIR, HUNTER AND
CHRISTIAN TEACHING LESSON 4.10
P-3
DUDA MATH
Goal and Vocab.
O By the end of this lesson Hunter, Christain and I will
teach you how to write a quadratic formula.
β’ Vocab you need to know for the dayβ¦
Best fitting quadratic model β The model
given by performing quadratic regression on a
calculator.
Important Formulas!
π¦ = π(π₯ β
β)2
+π
β’X & Y are found in the coordinates given in
the problem (usually 2nd set)
β’H & K are the 1st set usually
π¦ = π(π₯ β π)(π₯ β π)
β’As usual the X is the X coordinate and Y is
the Y coordinate.
β’P & Q are the coordinates given on the Y
axis
π¦ = ππ₯ 2 + ππ₯ + π
β’When you have 3 points given to you, you
use this formula and the xβs are the x
points, and same for the y.
β’A,B, and C you have to solve for.
Write a Quadratic Function in
Vertex Form
Y-Values
-5
-4
-3
-2
-1
6
5
4
3
2
1
0
-1 0
-2
-3
-4
Write a Quadratic Function in
Vertex form
O Example 1)
O Step 1 β Use π¦ = (π β β)2 + π
O Step 2 β Substitute for the βHβ and βKβ
π¦ = π(π₯ + 2)2 β 3
O Step 3 β substitute for βXβ and βYβ
5 = π(0 + 2)2 β 3
O Step 4 solve for βAβ, then later plug it in.
2=π
O So the quadratic formula for the parabola
is π¦ = 2(0 + 2)2 β 3
Your
Points
(-2,-3)
(0,5)
Write a Quadratic Function in
Intercept
form
Q (2,0)
P (-3,0)
Y-Values
-4
-2
0
-0.5 0
-1
-1.5
-2
-2.5
-3
-3.5
-4
-4.5
2
4
Write a Quadratic Function in
Intercept form
O Step 1 β use π¦ = π(π₯ β π)(π₯ β π)
O Step 2 β substitute for βPβ & βQβ
π¦ =π π₯+3 π₯β2
O Step 3 β substitute for βXβ & βYβ
β4 = π β2 + 3 β2 β 2
O Step 4 solve for βAβ and plug into equation
π=1
O So the equation for the Parabola is
π¦ = π₯ + 3 (π₯ β 2)
Your
points
P (-3,0)
Q (2,0)
X,Y (-2,-4)
CHECKPOINT
O Write a quadratic function whose graph has
the given Characteristics.
Write a Quadratic Function in
Standard Form
O Write a Quadratic function in standard form
that goes through these points
(-2,-6) (0,6) (2,2)
Shown on board
Power Point Directed By
Nir Taube
Hunter Osking
Christian Contrell
Power Point Produced By
Nir Taube
Starring
Nir Taube
Hunter Osking
Christian Contrell
Big D aka Darth Vader
Lesson