Domain Expansion: Vertex Form
What is the vertex form:
y=x^2+6x+3
y=(x+3)^2-6
Find the discriminant, then use it to find if there are any solutions:
-6x^2+7x+3=0
121; two real solutions
What are the solutions to this equation using the quadratic formula:
x^2-9x+20=0
x={5,4}
A coffee shop models daily revenue with
R(p) = -2p^2 + 44p
, where p is the price of a drink.
The shop earns $192 in revenue.
What drink prices produce this revenue?
$6 or $16
This television series often memed with math formulas, such as quadratic equations, to represent confusion, features talking aquatic life where the main protagonist is a fry cook that lives in a... pineapple???
What is Spongebob Squarepants?
What is the vertex form of:
y=x^2-6x+5
y=(x-3)^2-4
Find the discriminant, then use it to find if there are any solutions:
9x^2+6x+1=0
0; one real solution
What are the solutions to this equation using the quadratic formula:
x^2+3x-40=0
x={5,-8}
Ticket revenue for a school dance is given by
R(p) = -5p^2 + 100p
, where p is the price of a ticket.
The shop earns $320 in revenue.
What drink prices produce this revenue?
$4 or $16
The Batman, The Goliath, and the American Eagle are all names for this type of thrill-seeking attraction that utilizes quadratic functions to calculate their many gravity defying loopty loops.
What is a rollercoaster?
What is the vertex form of:
y-33=x^2+10x
y=(x+5)^2+8
Find the discriminant, then use it to find if there are any solutions:
-2x^2-x-1=0
-7; no real solutions
What are the solutions to this equation using the quadratic formula:
x^2-4x-14=-2
x={6,-2}
A soccer ball is kicked up into the air and follows the path of
h(t)=-8t^2+40t
, where t is the time in seconds the ball was in the air.
At what times is the ball 32 ft high?
t = 1 and t = 4
What is the Artemis II Space Mission?
What is the vertex of:
y=x^2-2x-5
Vertex: (1,-6)
Find the discriminant, then use it to find if there are any solutions:
x^2+5x=2x^2
25; two real solutions
What are the solutions to this equation using the quadratic formula:
2x^2+2x-12=0
x={2,-3}
A gym models monthly membership revenue as
R(p)=-4p^2+96p
, where p is the price of the membership.
Is a revenue of 320 possible? Use the discriminant to justify your answer.
Yes it is because the discriminant is 64, meaning there are two solutions that achieve a revenue of $320.
Developed and released in 2009, this mobile game featured enraged avian creatures that destroy buildings through quadratic trajectories to get to those greedy green pigs.
What is Angry Birds?
What is the vertex of:
y=x^2+4x
Vertex: (-2,-4)
Find the discriminant, then use it to find if there are any solutions:
4x^2=8x-4
0; one real solution
What are the solutions to this equation using the quadratic formula:
-6x^2-6x+16=4
x={-2,1}
A model rocket is shot into the air in a path of
h(t)=-16t^2+96t
, where t represents the time in seconds it is in the air before landing.
When does it reach maximum height? (Hint:Find your zeros)
It reaches maximum height in 3 seconds.
Dating back 2,000 years ago, the Babylonians used the quadratic formula to solve this problem that early colonists of the US and modern day adults alike complain about having to pay annually... or else the IRS comes knocking.
What are taxes?