Zero Product Property
If the product of two quantities (numbers) is zero, then at least one number must be zero. Two numbers may both also be zero.
What is the Zero Product Property?
As it relates to algebra, multiplication is to distribution as division is to _____?
What is factoring ?
This form identifies the following variables
a, h, k
What is vertex form?
This formula can be used to find the x-coordinate of the vertex of a parabola.
What is x= -b/2a?
The sketch of a parabola that is concaved up and that has a value of a>1
Answers will vary depending on vertex but overall parabola will open up and be narrow
If ab=0, then __=0, b=___, or a=b=___
What is a?
What is 0?
What is 0?
Before factoring a quadratic expression, this form is the original.
ax2+bx+c
What is Standard Form?
This is the graph of a quadratic.
What is a parabola?
The line that always passes through a parabola
What is the axis of symmetry?
Name two native DC artists and their top two songs.
Answers will vary
Find the solution to the following equation. (Make sure to show all your work)
(4n-1)(n+5)=0
1. Set both binomials equal to zero
4n-1=0 n+5=0
Take inverse of -1 (+1) and add to both sides of equal sign. Now left with 4n=1. Then take inverse of 4n (divide by 4)/ Now n=1/4
Take inverse of +5 (-5) and add to both sides of equal sign. Now n=-5
Explain how to solve the equation x2-7x+6=0
First factor the equation then use the Zero Product Property and the two binomial equations to solve for x.
Explain how the following parabola is affected (shifted) given this equation
y=2(X-3)2+8
This parabola will be narrow and open up because a>1 and a=2. It will shift 4 units right because h is 4 and 8 units up because k is 8
This is another way to phrase identifying the x-values of the vertex?
What are the roots?
The DC term for hot dogs?
What is a glizzy?
What is the sum of the two values that make the equation true?
(4m-1)(m+2)=3
Make both binomials equal to 3
4m-1=3 m+2=3
Set both equal to zero by taking the inverse of what's on the right side of the equal sign. 4m-4=0 m-1=0. Now use zero Product property.
4m-4=0 m-1=0
4m=4 m=1
m=1
One solution, m=1
For what values of x are the values of 5x2 and 14x-8 equivalent?
Make both equal to each other
5x2=14x-8
5x2-14x+8=0
(5x-4)(x-2)=0
5x-4=0 x-2=0
5x-4+4=0+4 x-2+2=0+2
5x=4 x=2
x=4/5
In vertex form, y=a(x-h)2+k, write an equation of a parabola that has vertex (-2,-1) and translates -5 units wide
y=-5(x+2)2-1
The roots of y=2x2+7x+3
(Zero Product Property)
0=(2x+1)(x+3)
2x+1=0 x+3=0
x=-1/2 x=-3
What are the roots of (-1/2,0) and (-3,0)?
This DC term describes confusion, frustration, or irritation due to another's actions?
What is being thrown off?
Layla solved the following inequality incorrectly. What did she do wrong?
Find the solutions to m(3m-1)(m2+1)=0
3m-1=0 OR m2+1=0
3m=1 m2=-1
m=1/3 no real solution
Because theres no real solutions for m2+1, then the only answer is m=1/3.
Although this solution is true, Layla forgot to take into account the m outside of the first binomial m(3m-1), therefore m=0 is also a valid solution.
After solutions are factored and zero product property is used, when graphing, these solutions are reflected across this axis.
What is the x-axis?
Create the equation of a parabola that is shifted up 2 and left 7 parabola
y=(x-1)2+6. How does this parabola open? How do you know?
h=1-7=-6
k=6+2=8
y=(x+6)2+8
This parabola opens up because a is positive.
The vertex of y=2x2+7x+3
x=-b/2a=-7/2(2)=-7/4
y=2(-7/4)2+7(-7/4)+3
y=2(-49/16)-49/4+3
y=(49/8)-(98/8)+24/8=-25/8 or -3 and 1/8
What is (-7/4, -25,8)?
Explain the difference between graphing a quadratic in standard form and identifying the vertex, width of parabola, variables, versus graphing a parabola in vertex form.
Standard: ax2+bx+c
With standard, first you must identify values of a,b,and c. The variable a determines the how wide or narrow parabola is (a>1, narrow, a<1 wide) Next, using the formula -b/2a, solve for the x coordinate of vertex by substituting variable values. Once x coordinate is identifies, plug back into the original standard form by substituting for x, to find y. Once (x,y) is found, you have the vertex.
Vertex form: a(x-h)2+k.
The value of (h,k) is the vertex. Keep in mind the h value changes once the inverse of whats in the parenthesis is taken. Ex: a(x-2)2+5, h=2 (inverse of -2) and vertex would be (2,5). Same rule applies with the a variable as standard form. If a>1, the parabola would be narrow and if a<1, wide parabola. Also, the direction in which the parabola opens is dependent upon if a is negative or positive.