( - lity) + ( - addi)

Equa + tion

Equation

( - een+a)

+ ( - gon + tic)Qua + dratic

Quadratic

( - ny+c)

+ ( - Educa)Func + tion

Function

Equation of

Quadratic Function

Activity

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

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

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

(-3,-29)

Equation 1

(-1,-5)

−𝟓=𝒂−𝒃+𝒄Equation 2

(1,3)𝟑=𝒂 (𝟏 )𝟐+𝒃 (𝟏 )+𝒄𝟑=𝐚+𝐛+𝒄

Equation 3

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

Equation 1 Equation 2 Equation 3

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

)

−𝟐𝟗=𝟗𝒂−𝟑𝒃+𝒄+𝟏𝟓=−𝟑𝒂+𝟑𝒃−𝟑𝒄

−𝟏𝟒=𝟔𝒂−𝟐𝒄Equation 4

3 3

Equation 5

𝑬𝒒 .𝟐−𝟓=𝒂−𝒃+𝒄

Eq. 4 Eq. 5 −𝟏𝟔=𝟖𝐚

𝒂=−𝟐

−𝟏𝟒=−𝟏𝟐−𝟐𝒄

Eq. 4 −𝟏𝟒=𝟔 (−𝟐)−𝟐𝒄

𝒄=𝟏

−𝟏𝟒+𝟏𝟐=−𝟐𝒄−𝟐−𝟐=

−𝟐𝒄−𝟐𝒄

Eq. 2 −𝟓=−𝟐−𝒃+𝟏

𝒃=𝟒

−𝟒=−𝒃−𝟒−𝟏=

−𝒃−𝟏

d) Write the equation of the quadratic function

𝒚=−𝟐 𝒙𝟐+𝟒 𝒙+𝟏

Finding the Equation

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

𝑺𝒕𝒆𝒑

(1,4)

𝑺𝒕𝒆𝒑

Equation 1

(-1,10)

𝑺𝒕𝒆𝒑

𝟏𝟎=𝒂(−𝟏)𝟐+𝒃(−𝟏)+𝒄

Equation 2

(2,4)

𝑺𝒕𝒆𝒑

Equation 3

Get the system of two linear equations with two variables.

𝑺𝒕𝒆𝒑

𝑺𝒕𝒆𝒑

Eq. 2

Equation 4

𝑺𝒕𝒆𝒑

Equation 5

+

22

𝟐𝟒=𝟔𝒂+𝟑𝒄

𝟐𝟒=𝟔𝒂+𝟑𝒄

Equation 4

Equation 5

33

c = 6

𝑺𝒕𝒆𝒑

Finding the value of a, b, and c .

𝑺𝒕𝒆𝒑

𝟏𝟒=𝟐𝒂+𝟐(𝟔)

𝟏𝟒−𝟏𝟐=𝟐𝒂𝟏𝟒=𝟐𝒂+𝟏𝟐

𝟐𝟐=

𝟐𝒂𝟐

a = 1

𝑺𝒕𝒆𝒑

𝟒−𝟏−𝟔=𝒃

b = -3

𝑺𝒕𝒆𝒑

Substitute the value of a, b, and c in

𝑺𝒕𝒆𝒑

𝑺𝒕𝒆𝒑

𝒚=(𝟏 ) 𝒙𝟐(−𝟑)𝒙+(𝟔)

Write your final answer in standard form of Quadratic Function.

𝑺𝒕𝒆𝒑

𝒚=𝒙𝟐−𝟑 𝒙+𝟔

𝑭𝒊𝒏𝒂𝒍 𝑨𝒏𝒔𝒘𝒆𝒓

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.

Seatwork

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.

Assignment

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

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

Prepared by:Ma. Antonette P. de Castro

Bachelor of Secondary Education

Mathematics Major