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.
• 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 = 𝑎(𝑥 −
ℎ)2
+𝑘
•X & Y are found in the coordinates given in
the problem (usually 2nd set)
•H & K are the 1st set usually
𝑦 = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
•As usual the X is the X coordinate and Y is
the Y coordinate.
•P & Q are the coordinates given on the Y
axis
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐
•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.
•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 = (𝑎 − ℎ)2 + 𝑘
O Step 2 – Substitute for the “H” and “K”
𝑦 = 𝑎(𝑥 + 2)2 − 3
O Step 3 – substitute for “X” and “Y”
5 = 𝑎(0 + 2)2 − 3
O Step 4 solve for “A”, then later plug it in.
2=𝑎
O So the quadratic formula for the parabola
is 𝑦 = 2(0 + 2)2 − 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 = 𝑎(𝑥 − 𝑝)(𝑥 − 𝑞)
O Step 2 – substitute for “P” & “Q”
𝑦 =𝑎 𝑥+3 𝑥−2
O Step 3 – substitute for “X” & “Y”
−4 = 𝑎 −2 + 3 −2 − 2
O Step 4 solve for “A” and plug into equation
𝑎=1
O So the equation for the Parabola is
𝑦 = 𝑥 + 3 (𝑥 − 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