Quadratics
Write down an example of a quadratic equation.
Answers vary.
Paul buys a car costing $17,000. If the car's value will depreciate (decrease) at a rate of 17% per year, write down an exponential function to represent how much money his car will be worth for t number of years.
f(t)=17,000(0.83)t
For f(x)=x2 and g(x)=3(x-1)2+7, identify all transformations that have taken to get from f(x) to g(x).
1) vertical stretch of 3
2) right 1
3) up 7
What is ln(e)?
1
***Terrific Triple***
If the team that chooses this gets the correct answer, they will earn triple points, while other teams who get it right earn the regular amount.
What is the expanded form of (6x-5)2?
36x2-60x+25
***Terrific Triple***
If the team that chooses this gets the correct answer, they will earn triple points, while other teams who get it right earn the regular amount.
Describe the number and type of solutions that a quadratic equation with a negative discriminant has.
2 non-real solutions
What is the asymptote of f(x)=3x-6
Horizontal asymptote at y=-6
***Steal from a team!***
If the team that chooses this problem gets it correct, then they will not only earn their points for this round, they will get to steal 300 points from a team of their choice!
For the function f(x)=a(x-h)+k, what will making a negative do to the function? In other words, what happens if we have f(x)=-a(x-h)+k?
The function is reflected across the x-axis.
Evaluate: log(100)-log(10)+log(1,000)
4
Factor to find all the solutions to the below equation:
x3-6x2+8x=0
Solutions: 0, 2 and 4
***Steal from a team!***
If the team that chooses this problem gets it correct, then they will not only earn their points for this round, they will get to steal 300 points from a team of their choice!
Find the solution(s) to the below quadratic equation.
4x2-4x=11
Solutions: 4+i and 4-i
***Terrific Triple***
If the team that chooses this gets the correct answer, they will earn triple points, while other teams who get it right earn the regular amount.
Solve: 363x > (1/216)5
x<5/2
For h(x)=4(x+6)2+9, what will the new function be if we shift the function 10 units to the right and 4 units down?
g(x)=4(x-4)2+5
***Steal from a team!***
If the team that chooses this problem gets it correct, then they will not only earn their points for this round, they will get to steal 300 points from a team of their choice!
Solve: log(4x-200)=2
x=300/4
***Steal from a team!***
If the team that chooses this problem gets it correct, then they will not only earn their points for this round, they will get to steal 300 points from a team of their choice!
Find the inverse of f(x).
f(x)= {(2,1), (5, 10), (4, 6), (6, 7), (0,0)}
f-1(x)= {(1,2), (10, 5), (6, 4), (7,6), (0,0)}
Find the solution(s) to the below quadratic equation.
f(x)=x2-8x+17=0
Solutions: 4+i and 4-i
Solve: (1/4)x-7=64
x=4
What will be the end behavior of the below function:
f(x)= -4x9+2x8-6x+3
As x approaches -infinity, f(x) approaches positive infinity.
As x approaches positive infinity, f(x) approaches negative infinity.
***Terrific Triple***
If the team that chooses this gets the correct answer, they will earn triple points, while other teams who get it right earn the regular amount.
Condense into a single log: log4(7)+6log4(x)-8log4(y)-2log4(z)
log4(7x6/y8z2)
Write the explicit formula for the given sequence: -6, 12, -24, 48, ...
an=-6(-2)n-1
Put the quadratic into vertex form and state the coordinates of the vertex.
y=x2+6x+36
Vertex Form: y=(x+3)2+27
vertex: (-3, 27)
Solve: 625-2=1253x+1
x=-11/9
If you have a function that is going to negative infinity in both the left and right directions, what does that tell us about what kind of leading coefficient and degree the function has?
The leading coefficient will be negative, and the degree will be even.
f(x)=500e-0.7t represents how many mg of Extra Strength Tylenol remain in the body after t hours. If May takes one Extra Strength Tylenol (which starts off with 500 mg), how long will it take for her to only have 20mg of the medicine left in her body? Round your answer to the nearest hour.
Multiply: (4+9i)(6-2i)
(your final answer must be simplified)
42+46i