This document provides examples and practice problems for transforming quadratic functions between standard and vertex form, finding the vertex, axis of symmetry, and maximum/minimum values. It begins with examples of transforming the functions f(x) = x^2 + 6x + 8 and f(x) = 2x^2 - 8x + 5 to vertex form. Later activities involve matching standard and vertex forms, finding the vertex and other properties for given functions, and multiple choice questions testing these skills. The document aims to help learn and practice competency in working with quadratic functions.

2. Leaning Competency:
1. Transform Quadratic function defined by f(x) = ax2 + bx + c into the
form f(x) = a(x – h)2 + k
2. Determine the vertex /turning point of the quadratic function
3. Find the axis of symmetry and maximum/ minimum value of the
quadratic function

3. Picachu, some of my
pokemon are caught by
Team Rockets. Return
my pokemon.
Haha You could only get
them if you solve
problems involving
vertex of a function
correctly.
Oh no! Ash,
We need to
help
them.Picka..
Picka…
You will
undergo 2 battle
stations for you
save your
pokemon

4. Picachu, I still remember the steps to
transform quadratic function in the
standardform f(x) = ax2 + bx + c to vertex
form f(x) = a(x – h)2 + k and from that we
could get the value vertex (h, k). But I already forget it. May you help me to
remind so that we can do it together?
Ex. #1 is when a = 1 say,
f(x) = x2 + 6x + 8
1. Complete the square
= (x2 + 6x) + 8
=(x2 + 6x + 9) + 8 – 9
2. Factor and Combine
F(x) = (x + 3)2 - 1
∴ vertex (- 3, -1)
Axis of symmetry = - 3
Minimum value = -1
Really Ash? As
easy as that. How
about if a is greater
than or less than
1?
Ex #2: Change f(x) =2x2 – 8x + 5 to
vertex form a>1.
1. Factor
= 2(x2 - 4x) + 5
2. Complete the square
= 2(x 2 – 4x + 4) + 5 – 8
3. Factor and combine
F(x) = 2(x – 2)2 – 3
∴ vertex (2, -3)
Axis of symmetry = 2
Minimum value = -3
Well, I learned a lot. I
am now ready for
Pokemon Battle.

5. Lets work
together to do
this
You have to
get 5 correct
anwers to
save
Bulbasur
Matching Type. Match the standard form in Column A with the
Corresponding vertex form in Column B.
A B
_____1. x2 + 4x + 3 a. f(x) = (x – 5)2 – 32
_____2. x2 – 10x - 7 b. f(x) = (x + 3/2)2 – 25/4
_____3. x2 + 3x - 4 c. f(x) = (x + 2)2 – 1
_____4. 3x2 – 6x + 10 d. f(x) = 3(x – 6)2 + 2
_____5. -5x2 + 3x + 8 e. f(x) = -5(x – 3/10)2 + 209/20
f. f(x) = 3(x – 1)2 + 7
Activity 1

6. With our
teamwork, I
am sure that
we could get
my pokemon.
At this time,
lets see if you
can still
perfectly get
it to save
Psyduck.
I. Find the vertex of the following quadratic equations and then,
determine the axis of symmetry (h) and maximum/minimum value (k).
1 f(x) = (x + 7)2 + 5
2. f(x) = 4(x – 1)2 + 9
3. f(x) = x2 + 2x – 11
4. f(x) = x2 + 5x + 6
5. f(x) = 3x2 – 12x – 7
Activity 2

7. I. Multiple Choice.
1. Express f(x) = x2 – 12x + 6 to f(x) = a(x – h)2 + k form,
a. f(x) = (x – 12)2 + 13 b. f(x) = (x+ 3)2 – 10 c. f(x) = (x – 6)2 – 30
2. What is the vertex of f(x) = 2(x + 5)2 + 2?
a. (5, 2) b. (-5, 2) c. (2, -5)
3. What is the axis of symmetry of f(x) = x2 + 2x – 3?
a. X= -4 b. x = -1 c .x = 2
4. What is the minimum value of f(x) = 3(x + 4)2 – 8?
a. 3 b. 4 c. -8
5. Find the turning point of f(x) = -2x2 – 8x + 7.
a. (-2, 15) b. (-8, 7) c. (-2, 7)
How much have you learned?

8. Think of this:
The height h in feet of a ball t seconds after
being tossed upwards is given by the
function h(t) = 84t – 16t2.
a. After how many seconds will hit the
ground?
b. What is the maximum height?

9. • Soledad Jose-Dilao, ed., et. Al, Advanced Algebra,
Trigonometry and Statistics

10. Activity 1
1. c
2. a
3. b
4. f
5. e
Activity 2
Axis of symmetry Maximum/minimum
value
1. (-7, 5) h = -7 k = 5
2. (1, 9) h = 1 k = 9
3. (-1, -12) h= -1 k = -12
4. (-5/2, -1/4) h = -5/2 k = -1/4
5. (2, -19) h = 2 k = -19
Assessment
1.c
2. b
3. b
4.c
5.a