Systems of Equations/Miscellaneous
Fill in the blank:
Time can't be __________
NEGATIVE!
Solve the equation:
(x + 2)(x - 1) = 0
Your answer should be in set notation
x = {-2, 1}
Simplify the expression.
Alejandro kicks a football. The graph shows the height of the football h in meters after t seconds. What is the football’s greatest height?
30.625 meters
Write the equation in vertex form of a parabola with a vertex of (-1, 5) that also passes through the points (2, -13) and (4, -45)
y = -2( x + 1 )2 + 5
What is the solution to the system?
y = x2 - 4x - 17
17 = x - y
(0, -17) AND (5, -12)
Graph the solution set to the inequality:
2x2 - 21x < -8x + 7
(Mrs. Wise will draw the answer)
Simplify.
(4 − 10i)(4 + 3i)
46 − 28i
Tamika throws a ball up in the air. The graph shows the height of the ball h in feet after t seconds. How long is the ball in the air?
3 seconds
A sled slides down a hill, accelerating as it goes. The table gives the time in seconds and the distance in meters the sled traveled.
Using regression methods, which equation best models the data?
A
Solve the system:
y = -3x2 - 46x - 159
x + y = 3
(-6, 9) AND (-9, 12)
Solve the quadratic equation:
4k2 + k - 5 = -k
Write your answer as a set using set notation
(-1 + sqrt(21)) / 4
(-1 - sqrt(21)) / 4
Simplify (−4 + 9i)(−7 − 2i)
46 − 55i
Find the focus and axis of symmetry of the equation y = 1/4 (x - 2)2 -1
Focus: (2, 0)
Axis of Symmetry: x = 2
Write a quadratic equation in standard form that matches the table below. Round to the nearest hundredth.
y = -.73x2 + 8.31x - 15.2
The area of a rectangle is 140.
The perimeter is 48.
What is the length and width of the rectangle?
14 and 10
Solve the quadratic equation.
x2 + 6x + 25 = 0
Write your answer using set notation.
-3 + 4i, -3 - 4i
Simplify (−7 − 10i) + (−4 + 2i)
−11 − 8i
Ava launches a toy rocket from a platform. The height of the rocket in feet is given by h(t) = −16t2 + 24t + 112 where t represents the time in seconds after launch. After how many seconds does the rocket hit the ground?
3.5 seconds
Write the equation in vertex form of a parabola that passes through the points (-1, 21), (2, 3), and (5, -3)
y = 2/3 ( x - 5)2 - 3
The area of rectangle is 44. The perimeter of the rectangle is 30.
What is the length and width of the rectangle?
11 and 4
Solve the quadratic equation.
9x2 - 5x + 2 = x
Write your answer as a solution set.
(1 + i) / 3
(1 - i) / 3
(−2 + 8i) − (−8 + 10i)
6 − 2i
List AND label the following features of the equation y = 1/2 (x + 3)2 + 2
Vertex
Focus
Axis of Symmetry
ALL x and y intercepts
Answers should be fractions or whole numbers.
Vertex: (-3, 2)
Focus: (-3, 5/2)
Axis of Symmetry: x = -3
y-intercept: (0, 13/2)
NO x-intercepts
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the height, to the nearest foot, at a time of 1 seconds.
291 feet