2nd

3. Illustrative Example 1:

4. Reasoning tells us that 3 straight cuts would
result to 6 pieces and 5 straight cuts to 10
pieces. In other words, pizza-cutting this way
can be described by the linear function
where is the number of straight cuts and ,
the number of pieces that result. The
corresponding table is shown below

5. Suppose what we want is the
greatest number of pieces for the
number of straight cuts we make.
Drawing diagrams to find out, the
results are shown below.

6. You will observe that the
corresponding table of values
will differ from that of the
equation

7.  Use the table to
get the greatest
number of pieces
for 6 straight cuts.

8.  Make a guess of the relation
between the variables.
Observation of the entries in the
table should have led you to see
the following relations:

9. Using for the number of
straight cuts and for the
maximum number of pieces,
we get

10. Does each table show a
pattern? Explain your answer?

11. a. Is quadratic
function useful in
real-life
situations?

12. b. How can
quadratic function
be used to solve
real-life problems?

13. There are many situations in the real
world that can be modeled or
mathematically described by the
quadratic function. Skill to do this can
be useful to make estimates of one
variable from known values of the
related variable or to make predictions
of the relationship between the same
two variables in a different situation.

14. Directions: Use values of
x and y to complete the
table below:
x 2 4 6 8 10 12 14
y 4 8 12 20

15. x 2 4 6 8 10 12 14
y 4 8 12 16 20 24 28

16. Directions: Use the table below
to determine the greatest
number of pieces for 6 straight
cuts.
x 0 1 2 3 4 5 6
y 1 2 4 7

17. x 0 1 2 3 4 5 6
y 1 2 4 7 11 16 22

18. Menggay maintains a
small retail store to help
support her family. Think
of the diagram below as
rows of bath soap.

20. b. Do you see a pattern in the
entries in the table?
c. Extend the table to rows 5,
6 and 7. What will be the
corresponding values for ?
d. Make a guess of the
equation of the function.

22. A quadratic function is
defined by the general
equation 𝑦 = 𝑥2
+ 𝑏𝑥 + 𝑐
where 𝑎 𝑏 and 𝑐 are real
numbers and 𝑎 ≠ 0

23. VS.