Solving Quadratic Equations
Quadratic Functions and Parabolas
Quadratic and Linear Equations in 2 Variables
Rational and Radical Expressions
Solving Rational and Radical Equations
100
Solve: 5k2 - 2k + 18 = 9k2 - 2k - 82
x = 5, x = -5
100
What is the equation of the axis of symmetry of: y = 2x2 + 4x - 5
x = -1
100
What is the discriminant of: y = -82 - 12x - 6
-48
100
Simplify and state any restrictions: (q - 4) / (16 - q2)
1 / (-4 - q) q not equal to 4, q not equal to -4
100
Solve: [ 5 / 4 ] + [1 / (2y) ] = [ 7 / 6 ]
y = -6
200
You may use your calculator: Solve: 5x2 + x + 8 = 3x2 + x + 30
x = 3.32 and x = -3.32
200
What is the equation of the axis of symmetry and the coordinates of the vertex of: y = -x2 + 6x - 1
x = 3 vertex: (3,8)
200
Use the discriminant to state how many points the two graphs of the following equations intersect: y = -x y = x2 + x + 1 In your answer include the value of the discriminant and the amount of points.
D = 0 1 point
200
Simplify: sqrt(3z) / sqrt(150z3)
5sqrt(2) / z
200
Solve: sqrt(2 - y) = y
y = 1 y = -2 is not a solution
300
You may use your calculator: Solve using the quadratic formula: -m2 - m + 10 = 10m - 1
m = .92 and m = -11.92
300
What is the equation of the axis of symmetry, the coordinates of the vertex of: Does the parabola open up or down? Is the vertex a maximum or a minimum? y = (-1/2)x2 + (1/3)x
x = (1/3) (1/3, 1/18) Opens down The vertex is a maximum
300
Solve: Find the intersections of the two graphs of the following equations: y = 5 - 4x - x2 y = 4x + 21
(-4, 5)
300
Simplify: [ 2 / (x+2) ] + [ 8 / (x2 - 4) ]
2 / (x-2)
300
Solve: [ 1 / (r - 3) ] + [ 1 / (r + 3) ] = [ 6 / (r2 - 9) ]
r = 3
400
Solve: 2b2 - b - 21 = 0
b = 7/2 and b = -3
400
What is the x-intercepts of: y = x2 - 3x + 2
(2,0) , (1,0)
400
Solve: Find the intersections of the two graphs of the following equations: x2 + y = 5 y - 3 = -(x - 4)
(-2, 1) and (3, -4)
400
Simplify: 2sqrt(75) + 4sqrt(12) - 2sqrt(18)
18sqrt(3) - 6sqrt(2)
400
Solve: [ 1 / (s + 3) ] = [ 4 / (s2 - 9) ]
s = 7 s = -3 is not a solution since it is a restriction.
500
Solve: r3 - 7x2 - 18r = 0
r = 0, r = r = 9, r = -2
500
What are the x-intercepts of: y = x2 - 2x + 1
(1,0)
500
You may use your calculator: Solve: Find the intersects of the two graphs of the equations: x2 + y = 25 x = y + 7
(5.18, -1.82) , ( -6.18, -13.18)
500
[ (3y + 12) / (y - 4 )] / [(y2 + 4y)/(2y - 8) ] + [ (y2 - 4) / (y2 + 6y + 9) ] / [ (y2 -2y - 8) / (y2 - y - 12) ]
(y2 + 4y + 18) / [y(y + 3)]
500
Two pipes can fill a storage tank in 9 hours. The larger pipe fills the tank three times as fast as the smaller one. How long would it take the smaller pipe alone to fill the tank?
36 hours
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