Solving by factoring
Quadratic formula
Solving by taking square roots
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100
Solve this quadratics by factoring.
x^2+2x=3
x2 + 2x - 3 = 0
= (x-1)(x+3) = 0
x = 1 or x = 3
100
Is this quadratic formula?
Yes
100
What do you have to do to solve quadratics equation by taking square roots after step 1?
Isolate the squared term. Then, you have to take the square roots both sides. After that, solve the square roots to get x alone.
100
What is the y-intercept of the function:
f(x)=4x²+2x-15
y-int: 15
100
A Math 2 class launches a bottle rocket from the top of the bleachers in the football stadium. The following functions represent the height of the rocket as a function of time.
h(t)=-16t²+32t+48; h(t)=-16(t-3)(t+1);-16(t-1)²+64
a) How high are the bleachers the rocket was launched from?
b) What is the maximum height reached by the rocket? When does it reach this height?
c) How long does it take the rocket to hit the ground?
a. 48 feet
b. 64 feet after 1 second
c. 3 seconds after launch
100
How many continents are there?
Double Points - Name them all.
7
North America, South America, Europe, Africa, Asia, Australia, Antarctica
100
Identify all of the transformations in the function:
f(x)=-(-x+5)^2+7
Reflection over the x-axis; Reflection over the y-axis; Translate left 5; Translate up 7
200
Write out the 4 steps to solve a quadratic by factoring.
Step 1. Write the equation in standard form and make sure it is equal to zero!
Step 2. Factor completely.
Step 3. Use the zero product property.
Step 4. Solve each factor to get the x.
200
Solve
x^2+4x-21=0
by using quadratic formula.
x=-7 or 3
200
Solve this equation by taking square roots.
x²+1=26
x²=25
x=-5, 5
200
What is the vertex of the function:
g(x) = 3(x - 5)²+2
Vertex: (5, 2)
200
The graph below shows the relationship between the height of a rocket and the time after it was launched.
a. What was the maximum height reached by the rocket?
b. How long was the rocket in the air?
c. How long did the height increase?
a. 250 feet
b. Approximately 7 seconds
c. Approximately 3 seconds
200
What is the official name of the # symbol? Note: It isn't hashtag or number symbol.
Pound or Octothorpe
200
Create the simplest equation that has the roots:
(3, 0), (-12, 0)
x^2+9x-36
300
Solve this quadratic equation by factoring.
x^2+16=10x
x2 - 10x + 16 =0
(x-2)(x-8)
x = 2 or x = 8
300
Solve
x^2-4x+5=0
using the quadratic formula.
x=2+-i
300
Solve this equation by taking square roots.
(x-4)²-16=0
x= 0, 8
300
What is the direction of opening of the function:
h(x)=-4(x-5)(x+7)
Concave Down
300
Find two consecutive even integers whose product is 224.
14 and 16
300
How many bones do sharks have?
None - they are all cartilage.
300
Create the equation that has the vertex (5, 6) and goes through the point (-1, -12).
400
Solve this quadratics equation by factoring.
x^2+7x+15=5
(x+2)(x+5)=0
x= -2 and x = -5
400
Solve
25x^2-20x=-13
by using quadratic formula.
x=(2+-3i)/5
400
Solve for x using the square root method.
2x^2+10=210
x=-10, 10
400
What is the y-intercept of the function:
k(x)=5(x - 9)²+14
y-int: 419
400
Highway safety engineers can use the formula d=0.05s²+1.1s to estimate the minimum stopping distance d in feet for a vehicle traveling s miles per hour. If a car is able to stop after 125 feet, what is the fastest it could have been traveling when the driver first applied the brakes?
Approximately 40 miles per hour
400
Which galaxy is closest to our own - the Milky Way - and will collide with us in about 4.5 billion years?
The Andromeda Galaxy
400
When in my birthday?
Closest Wins
June 6th, 1993
500
Solve:
77x^2-5x-12=0
x = -4/11, 3/7
500
Solve:
x^2-22x+211=0
x=11+-3isqrt(10)
500
Solve:
4x²-15=27
x=+-sqrt(42)
500
What is the vertex of the function:
j(x)=x²-6x+26
Vertex: (6, 26)
500
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time can be modeled by the function
h(t)=-16t^2+16t+480
, where t is the time in seconds and h is the height in feet. What height is Jason after 5 seconds has passed?
160 feet
500
What is the most manufactured product in human history?
Double Points - How many have been manufactured? My discretion on how close you have to be.
The Transistor - About 16 sextillion
500
Create the simplest equation that has the roots:
x=3+-2i