4.10 Write Quadratic Functions and Models

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Transcript 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 day…
Best fitting quadratic model – The model
given by performing quadratic regression on a
calculator.
Important Formulas!
𝑦 = π‘Ž(π‘₯ βˆ’
β„Ž)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
𝑦 = π‘Ž(π‘₯ βˆ’ 𝑝)(π‘₯ βˆ’ π‘ž)
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
𝑦 = π‘Žπ‘₯ 2 + 𝑏π‘₯ + 𝑐
β€’When you have 3 points given to you, you
use this formula and the x’s 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 – Use 𝑦 = (π‘Ž βˆ’ β„Ž)2 + π‘˜
O Step 2 – Substitute for the β€œH” and β€œK”
𝑦 = π‘Ž(π‘₯ + 2)2 βˆ’ 3
O Step 3 – substitute for β€œX” and β€œY”
5 = π‘Ž(0 + 2)2 βˆ’ 3
O Step 4 solve for β€œA”, then later plug it in.
2=π‘Ž
O So the quadratic formula for the parabola
is 𝑦 = 2(0 + 2)2 βˆ’ 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 – use 𝑦 = π‘Ž(π‘₯ βˆ’ 𝑝)(π‘₯ βˆ’ π‘ž)
O Step 2 – substitute for β€œP” & β€œQ”
𝑦 =π‘Ž π‘₯+3 π‘₯βˆ’2
O Step 3 – substitute for β€œX” & β€œY”
βˆ’4 = π‘Ž βˆ’2 + 3 βˆ’2 βˆ’ 2
O Step 4 solve for β€œA” and plug into equation
π‘Ž=1
O So the equation for the Parabola is
𝑦 = π‘₯ + 3 (π‘₯ βˆ’ 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
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