Solving Quadratics
Real World Application of Quadratics
Special Right Triangles
Probability
Compare/Contrast Quadratics
100
Solve the equation for x:
x^2 = 225
What is
x=\pm15
100
Ms. Gibala is trying to show her coach how high her vertical leap is. She starts her jump and is in the air for 5 whole seconds. She reached a maximum height of 12.5 feet in the air, like the swoll queen that she is.
What is the vertex of the function?
What is
(2.5, 12.5)?
100
Saul can see Spiderman about to jump off the spire (the pointy thing) on top of the Empire State Building. Saul wonders how tall the spire is. He stands 120 feet away from the base of the empire state building and takes the measurements shown in the diagram below.
What trigonometric ratio (sine, cosine, or tangent) or special right triangle shortcut can be used to solve for the height from the ground to the top of the spire?
What is
Tangent
100
Ms. Whitmer rolls a standard six-sided die. What is the probably that the die lands on a 3 or an even number?
What is
P(even or 3) = \frac{4}{6} = \frac{2}{3} = 0.67 = 67%
100
For the function f(x) below, identify if the vertex is a maximum or a minimum.
What is
Minimum vertex
200
Solve the equation for x:
x^2 + 12x - 15 = 0
What is
x=-6\pm\sqrt51
200
Dylan uses a catapult to launch a watermelon into the air from next to a river. He loads the catapult 3 feet away from the river. His friend times the distance of the watermelon from when it was launched until it lands to be 13 ft. The watermelon reaches a maximum height which is 37.5 ft.
What are the x-intercepts of the function? (In order to get points, you need to include both x-intercepts.)
What is
(3,0) and (16,0)
200
Saul can see Spiderman about to jump off the spire (the pointy thing) on top of the Empire State Building. Saul wonders how tall the spire is. He stands 120 feet away from the base of the empire state building and takes the measurements shown in the diagram below.
Solve for the height from the ground to the top of the spire.
What is
x=120tan(45) = 120\ feet
200
You go to Subway with your friends at lunch. Their sandwich orders are below.
What is the probability that your friends order a 6 inch sandwich?
What is
P(six) = \frac{6}{9} = \frac{2}{3} = 0.67 = 67%
200
For the function f(x) below, identify the y-intercept
What is
(0, -24)
300
Solve the equation for x:
x^2-10x+9=0
What is
x=9 \ AND \ x=1
300
Ms. Whitmer uses a cannon to shoot a huge marshmallow into the air from next to the Golden Gate Bridge. She loads the cannon 1 ft away from the bridge. Her friend calculated the distance of the marshmallow from when it is launched until it lands to be 12 ft. The marshmallow reaches a maximum height at the lowest part of the bridge which is 30.25 ft.
What is the vertex of the function?
What is
(7, 30.25)
300
Saul can see Spiderman about to jump off the spire (the pointy thing) on top of the Empire State Building. Saul wonders how tall the spire is. He stands 120 feet away from the base of the empire state building and takes the measurements shown in the diagram below.
What trigonometric ratio (sine, cosine, or tangent) or special right triangle shortcut can be used to solve for the height of the Empire State Building?
What is
Tangent
300
You go to Subway with your friends at lunch. Their sandwich orders are below.
What is the probability of ordering a turkey given it is a 6 inch sandwich?
What is
P(turkey\ given\ 6) = \frac{1}{6} = 0.17 = 17%
300
For the function f(x) below, identify whether the function is a vertical stretch or a vertical shrink.
What is
Vertical stretch by a factor of 2.
400
Solve the equation for m:
d=\frac{1}{2}rm^2
What is
m = \pm\sqrt\frac{3d}{r}
400
Alexis is standing on top of a 48 ft cliff overlooking the ocean. She throws a rock into the air. After three seconds, the rock reaches a maximum height of 75 ft. Five seconds later, the rock enters the ocean.
Write a function to model the situation.
What is
y=-3(x-3)^2+75
400
Saul can see Spiderman about to jump off the spire (the pointy thing) on top of the Empire State Building. Saul wonders how tall the spire is. He stands 120 feet away from the base of the empire state building and takes the measurements shown in the diagram below.
Solve for the height of the Empire State Building.
What is
x = 120tan(30) = 69.28\ feet
400
You go to Subway with your friends at lunch. Their sandwich orders are below.
What is the probability of ordering a footlong sandwich given it is veggie?
What is
P(foot\ long\ given\ veggie) = \frac{1}{3} = 0.33 = 33%
400
The function f(x) is represented by the graph below.
The function g(x) is represented by the following equation:
g(x) = -4(x-2)^2+25
Compare and contrast the vertex of f(x) and g(x). A comparison of the two functions should include whether the vertex is a maximum or minimum.
What is
The vertex of f(x) is a minimum while the vertex of g(x) is a maximum.
500
Mr. Wolf was trying to impress Ms. Gibala with his knowledge of solving literal equations. He was solving the following equation for d using the steps below.
g=\frac{1}{7}hd^2
Step 1:
g=\frac{1}{7}hd^2
Step 2:
7g = hd^2
Step 3:
\pm\sqrt(7g)=hd
Step 4:
\frac{\pm\sqrt(7g)}{h}=d
Ms. Gibala sees an error in Mr. Wolf's work. Where is the mistake and how would you fix it?
What is
Step 3 is incorrect. Mr. Wolf should have divided both sides by q before taking the square root. So the final answer should have been
d=\pm\sqrt\frac{7g}{h}
500
Mae is training her puppy to jump through hoops. She runs 5 ft from the wall and takes off into a jump! She jumps through a hoop at a height of 13.75 inches and lands on the ground 10 ft after she jumps.
Write a function to model the situation.
What is
y=-\frac{1}{2}(x-10)^2+12.5
500
Saul can see Spiderman about to jump off the spire (the pointy thing) on top of the Empire State Building. Saul wonders how tall the spire is. He stands 120 feet away from the base of the empire state building and takes the measurements shown in the diagram below.
How tall is JUST the spire?
What is
x=120 - 69.28 = 50.72\ feet
500
You go to Subway with your friends at lunch. Their sandwich orders are below.
P(turkey) =
\frac{3}{9}
P(turkey given 6 inch) =
\frac{1}{6}
Are {turkey} and {6 inch} independent?
What is
No turkey and 6 inch sandwiches are associated.
500
The function f(x) is represented by the graph below.
The function g(x) is represented by the following equation:
g(x) = -4(x-2)^2+25
Compare and contrast f(x) and g(x). A comparison of the two functions should include the vertical stretch/shrink.
What is
Both f(x) and g(x) have a vertical stretch. f(x) is stretched by a factor of 2 while g(x) is stretched by a factor of 4.