Solving Quadratic Equations/Complex Numbers
Quadratic Formula/Completing the Square
Solving Nonlinear Equations
MAX/BOBBY
Word Problems
100
Simplify the root √-49.
What is 7i?
100
Solve x²+30x+225=121 by Using Square Roots
Solutions are (4,26).
100
Solve the equation by graphing. x²+2x = -.5x² +2x
The solution is (0,0).
100
What kind of line would x²+6x+7>y represent on a graph?
What is a dotted line?
100
The sum of a number and its square is 72. Find the number.
The integer is either -9 or 8.
200
Simplify the root √-27.
3i√3?
200
S​olve when a does not = 1 2x­²-20x+60/2=0
The solution is 5±i√5.
200
Solve the nonlinear equation by graphing: y= x²-x-1 Equation 1 y= -2x-1 Equation 2
The solutions is at (0,-1).
200
What kind of line would x²-27x-19≥y represent on a graph?
What is a solid line?
200
A rectangle is 4 cm longer than it is wide, and its area is 117 sq. cm. Find its dimensions.
The length is 13 cm, and the width is 9 cm.
300
Simplify (3+9i)+ (15-i).
What is 18+8i?
300
Find the solutions of x²-3x-4 using the quadratic formula.
What is (4, -1).
300
Solve the nonlinear system by substitution. x²+x-y = -1 Equation 1 x+y = 4 Equation 2
The solutions are (-3,7) and (1,3).
300
Example 1) Graph y > -x²-2x-1.
See notes sheet.
300
A painter is making a rectangular canvas for her painting. She wants the length of the canvas to be 4 ft more than twice the width of the canvas. The area of the canvas must be 30 sq. ft. What should the dimensions of the canvas be?
The canvas should be 3 ft. by 10 ft.
400
Solve algebraically 3x²+9=0.
No real solutions. (3i)
400
Find the discriminant of x²-3x-4 and tell of how many/ what kind of solutions the equations possesses.
What is two real solutions?
400
Solve the nonlinear equation using elimination x²-5x-y = -2 Equation 1 x²+2x+y = 0 Equation 2
There are no solutions.
400
Example 2) Graph y < -x² + 3 and y ≥ x ²+ 2x - 3.
See notes sheet.
400
Two ships leave port, one sailing east and the other south, Some time later they are 17 mi apart, with the eastbound ship 7 mi farther from port than the southbound ship. How far is each from port?
The eastbound ship is 15 mi away, and the southbound ship is 8 mi away.
500
Solve -2x²-2=4x by graphing.
What is -1?
500
Solve x­²-18x+5=0 using completing the square.
The solution is 9±2√19.
500
Solve the system by elimination. 2x²-8x+y = -5 2x²-16x-y = -31
The solution is (3,1).
500
Example 1) Solve x² - 3x - 4 < 0 algebraically
Solutions are (4,-1)... see notes sheet for line graph.
500
You have made a rectangular stained glass window this is 2 feet by 4 feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of the border be?
The width should be a 1/2 foot or 6 inches.
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