This document provides instructions for finding the equation of a quadratic function given a table of values. It involves the following steps: 1) Substitute ordered pairs from the table into the quadratic function equation y=ax^2 + bx + c to obtain a system of equations. 2) Solve the system of equations to find the values of a, b, and c. 3) Write the quadratic function equation in the form y=ax^2 + bx + c, using the values obtained for a, b, and c. The worked example finds the equation y=x^2 - 3x + 6 for the quadratic function represented by the table.

2. ( - lity) + ( - addi)
Equa + tion
Equation

3. ( - een+a)
+ ( - gon + tic)
Qua + dratic
Quadratic

4. ( - ny+c)
+ ( - Educa)
Func + tion
Function

6. Activity

7. 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 3
Y -29 -5 3 1 -5

8. a)Substitute one by one the
three (3) ordered pairs (x,y) in
𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄.
b) What are the three (3)
equations you came up with?
________, _________, __________
c)Solve for the values of a, b,
and c.
c)Write the equation of the quadratic
function 𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄
X -3 -1 1 2 3
Y -29 -5 3 1 -5

9. a)Substitute one by one the
three (3) ordered pairs (x,y)
in 𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄.
−𝟐𝟗 = 𝒂(−𝟑) 𝟐 + 𝒃(−𝟑) + 𝒄
(-3,-29)
−𝟐𝟗 = 𝟗𝒂 − 𝟑𝒃 + 𝒄
Equation 1

10. −𝟓 = 𝒂(−𝟏) 𝟐 + 𝒃(−𝟏) + 𝒄
(-1,-5)
−𝟓 = 𝒂 − 𝒃 + 𝒄
Equation 2
(1,3)
𝟑 = 𝒂 𝟏 𝟐 + 𝒃 𝟏 + 𝒄
𝟑 = 𝐚 + 𝐛 + 𝒄
Equation 3

11. b.)What are the three (3)
equations you came up
with?
Equation 1
−𝟐𝟗 = 𝟗𝒂 − 𝟑𝒃 + 𝒄
Equation 2
−𝟓 = 𝒂 − 𝒃 + 𝒄
Equation 3
𝟑 = 𝒂 + 𝒃 + 𝒄

12. c.) Solve for the values
of a, b, and c.
𝑬𝒒. 𝟏 − 𝟐𝟗 = 𝟗𝒂 − 𝟑𝒃 + 𝒄
𝑬𝒒. 𝟐 (−𝟓 = 𝒂 − 𝒃 + 𝒄)
−𝟐𝟗 = 𝟗𝒂 − 𝟑𝒃 + 𝒄
+𝟏𝟓 = −𝟑𝒂 + 𝟑𝒃 − 𝟑𝒄
−𝟏𝟒 = 𝟔𝒂 − 𝟐𝒄
Equation 4
−3 −3

13. Equation 5
𝑬𝒒. 𝟐 − 𝟓 = 𝒂 − 𝒃 + 𝒄
𝑬𝒒. 𝟑 +𝟑 = 𝒂 + 𝒃 + 𝒄
−𝟐 = 𝟐𝐚 + 𝟐𝒄
Eq. 4 −𝟏𝟒 = 𝟔𝒂 − 𝟐𝒄
Eq. 5 + −𝟐 = 𝟐𝐚 + 𝟐𝒄
−𝟏𝟔 = 𝟖𝐚
𝒂 = −𝟐
−𝟏𝟔
𝟖
=
𝟖𝒂
𝟖

14. −𝟏𝟒 = −𝟏𝟐 − 𝟐𝒄
Eq. 4 −𝟏𝟒 = 𝟔𝒂 − 𝟐𝒄
−𝟏𝟒 = 𝟔(−𝟐) − 𝟐𝒄
𝒄 = 𝟏
−𝟏𝟒 + 𝟏𝟐 = −𝟐𝒄
−𝟐
−𝟐
=
−𝟐𝒄
−𝟐𝒄

15. −𝟓 + 𝟐 − 𝟏 = − 𝒃
Eq. 2 −𝟓 = 𝒂 − 𝒃 + 𝒄
−𝟓 = −𝟐 − 𝒃 + 𝟏
𝒃 = 𝟒
−𝟒 = − 𝒃
−𝟒
−𝟏
=
−𝒃
−𝟏

16. d) Write the
equation of
the quadratic
function
𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄.
𝒚 = −𝟐𝒙 𝟐
+ 𝟒𝒙 + 𝟏

17. Finding the
Equation

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

19. (1,4)
𝑺𝒕𝒆𝒑
𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄
𝟒 = 𝒂(𝟏) 𝟐+ 𝒃(𝟏) + 𝒄
Equation 1
𝟒 = 𝒂 + 𝒃 + 𝒄

20. (-1,10)
𝑺𝒕𝒆𝒑
𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄
𝟏𝟎 = 𝒂(−𝟏) 𝟐 + 𝒃(−𝟏) + 𝒄
Equation 2
𝟏𝟎 = 𝒂 − 𝒃 + 𝒄

21. (2,4)
𝑺𝒕𝒆𝒑
𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄
𝟒 = 𝒂(𝟐) 𝟐 + 𝒃(𝟐) + 𝒄
Equation 3
𝟒 = 𝟒𝒂 + 𝟐𝒃 + 𝒄

22. Get the system of two
linear equations with
two variables.
𝑺𝒕𝒆𝒑

23. 𝑺𝒕𝒆𝒑
Eq. 1 4 = 𝑎 + 𝑏 + 𝑐
Eq. 2 𝟏𝟎 = 𝒂 − 𝒃 + 𝒄
Equation 4
𝟏𝟒 = 𝟐𝒂 + 𝟐𝒄

24. 𝑺𝒕𝒆𝒑
Eq. 2 ( 𝟏𝟎 = 𝒂 − 𝒃 + 𝒄)
𝟐𝟎 = 𝟐𝒂 − 𝟐𝒃 + 𝟐𝒄
Equation 5
+ 𝟒 = 𝟒𝒂 + 𝟐𝒃 + 𝒄
22
𝟐𝟒 = 𝟔𝒂 + 𝟑𝒄

25. 𝟏𝟒 = 𝟐𝒂 + 𝟐𝒄
𝟐𝟒 = 𝟔𝒂 + 𝟑𝒄
Equation 4
Equation 5

26. Eq. 4 (14 = 2𝑎 + 2𝑐)
𝟒𝟐 = 𝟔𝒂 + 𝟔𝒄
33
𝟏𝟖 = 𝟑𝒄
−𝟐𝟒 = −𝟔𝒂 − 𝟑𝒄
𝟏𝟖
𝟑
=
𝟑𝒄
𝟑
c = 6
𝑺𝒕𝒆𝒑

27. Finding the
value of
a, b, and c .
𝑺𝒕𝒆𝒑

28. Eq. 4 14 = 2𝑎 + 2𝑐
𝟏𝟒 = 𝟐𝒂 + 𝟐(𝟔)
𝟏𝟒 − 𝟏𝟐 = 𝟐𝒂
𝟏𝟒 = 𝟐𝒂 + 𝟏𝟐
𝟐
𝟐
=
𝟐𝒂
𝟐
a = 1
𝑺𝒕𝒆𝒑

29. Eq. 1 𝟒 = 𝒂 + 𝒃 + 𝒄
𝟒 = 𝟏 + 𝒃 + 𝟔
−𝟑 = 𝒃
𝟒 − 𝟏 − 𝟔 = 𝒃
b = -3
𝑺𝒕𝒆𝒑

30. Substitute the value of
a, b, and c in
𝒚 = 𝒂𝒙 𝟐
+ 𝒃𝒙 + 𝒄
𝑺𝒕𝒆𝒑

31. 𝒚 = 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄
𝑺𝒕𝒆𝒑
𝒚 = 𝟏 𝒙 𝟐
(−𝟑)𝒙 + (𝟔)

32. Write your final answer
in standard form of
Quadratic Function.
𝑺𝒕𝒆𝒑

33. 𝒚 = 𝒙 𝟐
− 𝟑𝒙 + 𝟔
𝑭𝒊𝒏𝒂𝒍 𝑨𝒏𝒔𝒘𝒆𝒓

34. Remember
You 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.

35. Seatwork

36. 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.

38. Assignment

39. 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

41. Prepared by:
Ma. Antonette P. de Castro
Bachelor of Secondary Education
Mathematics Major