Multiplying and Factoring
Modeling
Quadratic Inequalities
Circles and Transformations
Absolute Value Equations and Inequalities
100
3x(x - 8)
3x2-24x
100
Physics students fired a ball off of the top of a building and tracked its height above the ground. They then modeled the height, in meters, above the ground as a function of time, in seconds, since it was fired. The equation they determined was h(t) = -10t2 + 15t + 25.
Calculate h(0) and tell what it represents about the ball.
h(0) = 25. It represents that at time 0, the ball was 25 meters above the ground. The top of the building is 25 meters tall.
100
x2 - 4 > 0
Find the solution set for the inequality using set builder notation
{x|x < -2 or x > 2}
100
Give the center and radius of the circle given by the equation (x + 3)2 + (y - 4)2 = 25
center: (-3,4)
radius: 5
100
Where is the vertex of the function y = |x - 3| + 2
(3, 2)
200
(x - 7)(4x + 9)
4x2 + 9x - 28x - 63 = 4x2 - 19x - 63
200
Physics students fired a ball off of the top of a building and tracked its height above the ground. They then modeled the height, in meters, above the ground as a function of time, in seconds, since it was fired. The equation they determined was h(t) = -10t2 + 15t + 25.
Determine the greatest height of the ball and the time it reaches this height.
The greatest height is 30.625 meters. It occurs after 0.75 seconds.
200
x^2 - 5x - 36 <= 0
Write your answer in interval notation
[-4, 9]
200
Give the transformations in order: f(x) --> 4f(x + 3) - 5
left 3, vertical stretch by a factor of 4, down 5
200
Solve 3|x - 4| + 11 < 32
{x| -3 < x < 11}
300
216x2 + 387x + 45
9(8x + 1)(3x + 5)
300
Physics students fired a ball off of the top of a building and tracked its height above the ground. They then modeled the height, in meters, above the ground as a function of time, in seconds, since it was fired. The equation they determined was h(t) = -10t2 + 15t + 25.
Determine the time it takes for the object to hit the ground.
The object takes 2.5 seconds to hit the ground. This can be found using the positive x intercept of the graph/equation.
300
7x2 + 4x + 3 > 3x2 + 4x + 4
Find the solution set. Represent your answer on a number line.
open dots at +0.5 and -0.5. Arrows outward.
{x|x < -0.5 or x > 0.5}
300
write the equation of a circle with center (5,6) and point on the circle of (10, -6)
(x - 5)2 + (y - 6)2= 169
300
Solve |2x - 1| = x + 13
x = -4, 14
400
Factor Completely by Grouping:
9x3 + 27x2 - 16x - 48
9x2(x + 3) - 16(x + 3)
(9x2 - 16)(x + 3)
Final Answer: (3x - 4)(3x + 4)(x + 3)
400
Physics students fired a ball off of the top of a building and tracked its height above the ground. They then modeled the height, in meters, above the ground as a function of time, in seconds, since it was fired. The equation they determined was h(t) = -10t2 + 15t + 25.
If you are the physics student, you can only see the ball when it is at a height greater than where it started. For how long can you see the ball?
You can only see the ball from the top of the building for 1.5 seconds. (find the intersection of h(t) and the line y = 25)
400
Graph the inequality y < 4x - x2
400
A function has a domain of [-5,16] and a range of [-20, 2]. What is the domain and range of the function after the transformations given by 0.5f(3x - 5) + 7?
Domain: [0, 7]
Range: [-3, 8]
400
Solve
|2x - 1| >= x - 11
all real numbers
(both -10 and 4 are extraneous solutions. Had to test if it is all real numbers or no solution)