day 17 – section 6.3, 6.5 (1)
TRANSCRIPT
DAY 17 – SECTIONS 6.3, 6.5
Review:
Factor the following
1. 3𝑥! − 𝑥 − 4
2. −6𝑥! + 11𝑥 − 3
Section 6.3 – Factor Special Products
1. Factor Difference of Two Squares
o (a – b)(a + b). What is the pattern?
(a – b)(a + b) = a2 – b2 Factor completely:
o 9z2 – 16
o 9z2 – 16p2
o 9z2y2 – 16y2
4w2v4 – 49x2
Section 6.5 – Polynomial Equations
1. Review: Solving Linear Equations.
o What does it mean to be a solution to a linear equation?
Ex/. y = 2x + 4
Is (2, 2) in the solution set?
Is (0, 4) in the solution set?
2. Define Polynomial Equation:
o A polynomial equation is an equation that contains a polynomial expression.
The degree of the polynomial equation is the degree of the polynomial.
o Quadratic equation – ax2 + bx + c = 0 where a, b, c, are real numbers and a is not 0.
▪ Why is it important that a ≠ 0?
o What degree is a quadratic?
o Examples of degree 2 or quadratic: What do they all have in common?
▪ u(u + 1) = 2
▪ (2 - x)x = 0
▪ x2 + 3x = -2
▪ x2 - x - 6 = 0
3. Zero Product Property
o a * b = 0
o What is a solution to this equation? What is another one?
o What can we conclude about a and b, if anything?
o Consider the equation a*b = 4.
o What is a solution to this equation? What’s another one?
o What can we conclude about a and b, if anything?
o How is this different from the equation above?
o
o Solving Factored Quadratic Equations:
Examples:
o (x - 3) (x + 2) = 0
o (2x + 1)x = 0
o (3 - m) (3 + m) = 0
o !!"− 10& !!
"+ 10& = 0
o (x - 6)2 = 0
4. Solve Quadratic Equations by Factoring
o 9x2 + 6x + 1 = 0
o 9x2 – 6x + 1 = 0
o 4x2 + 20x + 25 = 0
o 4x2 - 20x + 25 = 0
o 8x3 + 40x2 + 50x = 0
o 9 – 4x2 = 0
o "!
#$− 25 = 0
5. Zero of a Function
o For any function f, if f(x) = 0, then x is a zero of the function.
o What is the geometric connection with f(x) = 0? Where is this f(x) located on the Cartesian
Coordinate System? What is the ordered pair?
o x-intercept and y-intercept.
Sketch examples of intercepts here:
Ex/ f(x) = x2 - 2x + 1
o For the following examples of quadratics, find the zeroes, or x – intercepts (ordered pair).
Ex/ f(x) = (x – 2) (x+ 3)
Ex/ f(x) = 8x2 – 2x – 3
Ex/ f(x) = – 8x2 – 10x + 3
2. Applications –
Ex/ John is a garden designer. His client has requested him to build a rectangular garden with an area of 14
square feet. The client also requested that the length of the garden be 3 less than twice the width. Find the
length and width of the garden.
Ex/ Determine the positive number whose square exceeds twice its value by 15.
Ex/ Gianna is going to throw a ball from the top floor of her middle school.
The function h(t) = −16t2 +32t + 48 models the height, h, of the ball above the ground as a function of
time, t.
Find:
(a) the height the ball will be at t = 1 seconds.
(b) the time(s) the ball will be 48 feet above the ground.
(c) when the ball hits the ground.
Ex/ Carolyn is going to throw a ball from the top floor of her middle school. The function
h(t) = −16t2 + 16t + 192 models the height, h, of the ball above the ground as a function of time t. (a) Find the time(s) when the ball's height is 192 feet. (b) Find the time when the ball hits the ground.
