My finale MAD. Antonette

41

Transcript of My finale MAD. Antonette

Page 1: My finale MAD. Antonette
Page 2: My finale MAD. Antonette

( - lity) + ( - addi)

Equa + tion

Equation

Page 3: My finale MAD. Antonette

( - een+a)

+ ( - gon + tic)Qua + dratic

Quadratic

Page 4: My finale MAD. Antonette

( - ny+c)

+ ( - Educa)Func + tion

Function

Page 5: My finale MAD. Antonette

Equation of

Quadratic Function

Page 6: My finale MAD. Antonette

Activity

Page 7: My finale MAD. Antonette

The table of values below describes a quadratic function. Find the equation of the quadratic function by following the given procedure. Use these three ordered pairs (-3,-29),(-1,-5) and (1,3) from the table of values.

X -3 -1 1 2 3Y -29 -5 3 1 -5

Page 8: My finale MAD. Antonette

a)Substitute one by one the three (3) ordered pairs (x,y) in

b) What are the three (3) equations you came up with?________, _________, __________c) Solve for the values of a, b, and c.d)Write the equation of the quadratic function

X -3 -1 1 2 3Y -29 -5 3 1 -5

Page 9: My finale MAD. Antonette

a)Substitute one by one the three (3) ordered pairs (x,y) in

(-3,-29)

Equation 1

Page 10: My finale MAD. Antonette

(-1,-5)

βˆ’πŸ“=π’‚βˆ’π’ƒ+𝒄Equation 2

(1,3)πŸ‘=𝒂 (𝟏 )𝟐+𝒃 (𝟏 )+π’„πŸ‘=𝐚+𝐛+𝒄

Equation 3

Page 11: My finale MAD. Antonette

b.)What are the three (3) equations you came up with?

Equation 1 Equation 2 Equation 3

Page 12: My finale MAD. Antonette

c.) Solve for the values of a, b, and c.

)

βˆ’πŸπŸ—=πŸ—π’‚βˆ’πŸ‘π’ƒ+𝒄+πŸπŸ“=βˆ’πŸ‘π’‚+πŸ‘π’ƒβˆ’πŸ‘π’„

βˆ’πŸπŸ’=πŸ”π’‚βˆ’πŸπ’„Equation 4

3 3

Page 13: My finale MAD. Antonette

Equation 5

𝑬𝒒 .πŸβˆ’πŸ“=π’‚βˆ’π’ƒ+𝒄

Eq. 4 Eq. 5 βˆ’πŸπŸ”=πŸ–πš

𝒂=βˆ’πŸ

Page 14: My finale MAD. Antonette

βˆ’πŸπŸ’=βˆ’πŸπŸβˆ’πŸπ’„

Eq. 4 βˆ’πŸπŸ’=πŸ” (βˆ’πŸ)βˆ’πŸπ’„

𝒄=𝟏

βˆ’πŸπŸ’+𝟏𝟐=βˆ’πŸπ’„βˆ’πŸβˆ’πŸ=

βˆ’πŸπ’„βˆ’πŸπ’„

Page 15: My finale MAD. Antonette

Eq. 2 βˆ’πŸ“=βˆ’πŸβˆ’π’ƒ+𝟏

𝒃=πŸ’

βˆ’πŸ’=βˆ’π’ƒβˆ’πŸ’βˆ’πŸ=

βˆ’π’ƒβˆ’πŸ

Page 16: My finale MAD. Antonette

d) Write the equation of the quadratic function

π’š=βˆ’πŸ π’™πŸ+πŸ’ 𝒙+𝟏

Page 17: My finale MAD. Antonette

Finding the Equation

Page 18: My finale MAD. Antonette

Get the system of three linear equations in a, b, and c.

𝑺𝒕𝒆𝒑

Page 19: My finale MAD. Antonette

(1,4)

𝑺𝒕𝒆𝒑

Equation 1

Page 20: My finale MAD. Antonette

(-1,10)

𝑺𝒕𝒆𝒑

𝟏𝟎=𝒂(βˆ’πŸ)𝟐+𝒃(βˆ’πŸ)+𝒄

Equation 2

Page 21: My finale MAD. Antonette

(2,4)

𝑺𝒕𝒆𝒑

Equation 3

Page 22: My finale MAD. Antonette

Get the system of two linear equations with two variables.

𝑺𝒕𝒆𝒑

Page 23: My finale MAD. Antonette

𝑺𝒕𝒆𝒑

Eq. 2

Equation 4

Page 24: My finale MAD. Antonette

𝑺𝒕𝒆𝒑

Equation 5

+

22

πŸπŸ’=πŸ”π’‚+πŸ‘π’„

Page 25: My finale MAD. Antonette

πŸπŸ’=πŸ”π’‚+πŸ‘π’„

Equation 4

Equation 5

Page 26: My finale MAD. Antonette

33

c = 6

𝑺𝒕𝒆𝒑

Page 27: My finale MAD. Antonette

Finding the value of a, b, and c .

𝑺𝒕𝒆𝒑

Page 28: My finale MAD. Antonette

πŸπŸ’=πŸπ’‚+𝟐(πŸ”)

πŸπŸ’βˆ’πŸπŸ=πŸπ’‚πŸπŸ’=πŸπ’‚+𝟏𝟐

𝟐𝟐=

πŸπ’‚πŸ

a = 1

𝑺𝒕𝒆𝒑

Page 29: My finale MAD. Antonette

πŸ’βˆ’πŸβˆ’πŸ”=𝒃

b = -3

𝑺𝒕𝒆𝒑

Page 30: My finale MAD. Antonette

Substitute the value of a, b, and c in

𝑺𝒕𝒆𝒑

Page 31: My finale MAD. Antonette

𝑺𝒕𝒆𝒑

π’š=(𝟏 ) π’™πŸ(βˆ’πŸ‘)𝒙+(πŸ”)

Page 32: My finale MAD. Antonette

Write your final answer in standard form of Quadratic Function.

𝑺𝒕𝒆𝒑

Page 33: My finale MAD. Antonette

π’š=π’™πŸβˆ’πŸ‘ 𝒙+πŸ”

π‘­π’Šπ’π’‚π’ π‘¨π’π’”π’˜π’†π’“

Page 34: My finale MAD. Antonette

RememberYou can use any ordered pairs from the

given table of values. Using different ordered pairs, you will got different system of linear equation but you will arrive in the same answer for your quadratic function.

Page 35: My finale MAD. Antonette

Seatwork

Page 36: My finale MAD. Antonette

Matching Type Solve the column A and match it to its equivalent answer in column B, then match the column B to its equivalent procedures of finding the equation of quadratic function in column C.

Page 37: My finale MAD. Antonette
Page 38: My finale MAD. Antonette

Assignment

Page 39: My finale MAD. Antonette

Perform the five steps to find the equation of the quadratic function represented by the table of values below.

Write your answer in one whole sheet of paper together with your solution

X -3 -2 -1 0 1 2 3

y 2 1 2 5 10 17 26

Page 40: My finale MAD. Antonette

Every time you subtract negative (-) from your life, you make room for more positive (+)

Page 41: My finale MAD. Antonette

Prepared by:Ma. Antonette P. de Castro

Bachelor of Secondary Education

Mathematics Major