LESSON 1 – MAXIMA AND MINIMA (COMPLETING THE SQUARE)
STANDARD FORM
2


𝑦 = 𝑎𝑥 + 𝑏𝑥 + 𝑐
𝑎 is the stretch or compression
factor.
𝑐 is the initial value
COMPLETING THE
SQUARE
VERTEX FORM


𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
𝑎 is the stretch or compression
factor.
(ℎ, 𝑘) is the vertex
PERFECT SQUARE TRINOMIALS
Example ①
Example ②
Expand
a) (𝑥 + 5)2
Factor the following perfect square trinomials
a) 𝑥 2 + 6𝑥 + 9
b) 𝑥 2 − 2𝑥 + 1
Completing the Square:
𝑏 2
𝑐= ( )
2
Example ③
b) (𝑥 − 3)2
Adding a constant to a quadratic
expression to form a perfect square
trinomial.
Determine the missing number to create a perfect square trinomial.
a) 𝑥 2 + 8𝑥 + _____
b) 𝑥 2 − 14𝑥 + _____
c) 𝑥 2 + 1.4𝑥 + _____
d) 𝑥 2 − 2 𝑥 + _____
5
Example ① Determine the vertex of each quadratic relation by completing the square.
State the vertex, axis of symmetry, the maximum or minimum value and the values y may take.
a) 𝑦 = 𝑥 2 – 8𝑥 + 4
1
𝑎=1
Write the value of 𝑏 = ________
Divide b by 2 and square the result
𝑏 2
2
(2) = ______
Add and subtract the value from 1
3
Factor the first three terms (it will be a perfect
square trinomial)
1
Factor 𝑎 from the first and second terms ONLY.
2
Write the NEW value of 𝑏 = ________
Divide b by 2 and square the result
b) 𝑦 = −2𝑥 2 + 8𝑥 + 3
a≠1
𝑏 2
(2) = ______
c) 𝑦 + 3 = 𝑥 2 + 4𝑥
3
Add and subtract the value from 1
4
Multiply the last term by ‘a’
5
Factor the three terms inside the brackets it will be
a perfect square trinomial)
d) 𝑦 = −6𝑥 + 3𝑥 2