Quadratic Systems

Which of the following equations could be used to solve:
y = x² + 3x - 5
y = x + 3

• x² - 3x + 5 = x - 3
• x² + 3x - 5 = x + 3
• x² + 3x - 5 + x + 3 = 0
• x² + 3x - 5 = 0

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

• (-4, 2) and (-1, 5)
• (-4, -1) and (2, 5)
• (2, -1 and (-4, 5)
• (-4, 1) and (2, -1)

Find the solution:
y = x² - 4x + 6
y = x + 2

• (3, 1) and (6, 4)
• (-1, 1) and (4, 2)
• (1, 3) and (4, 6)
• (1, 4) and (3, 6)

• A
• B
• C
• D

Amy throws a quarter from the top of a building at the same time that a balloon is released from the ground. The equation describing the height y above ground of the quarter in feet is y = 64 - 2x² , where x is the time in seconds. The equation describing the elevation of the balloon in feet is y = 6x + 8, where x is the time in seconds. After how many seconds will the balloon and quarter pass each other?Check your solution for reasonableness.

• x=-7 and x=4
• 7 seconds
• 4 seconds
• 4 and 7 seconds

Determine the number of solutions to the given linear-quadratic function.

• 0 solutions
• 1 solution
• 2 solutions
• 3 solutions

The system of a linear and a quadratic function can have the following number of solutions, EXCEPT

• No solution
• 1 solution
• 2 solutions
• more than 2 solutions

Determine the solution to the given linear-quadratic function.

• (3, -1)
• (-3, 0)
• (2, -3)
• (-3, 2)

How many solutions can a line and a parabola have?

• No solutions, 1 solution
• No solutions, 1 solution, 2 solutions
• 1 solution
• No solutions, 1 solution, 2 solutions, infinite solutions

Solve the system algebraically.
y²-26=-x²
x-y=6

• (-1,-5) and (-5,-1)
• (-1,5) and (-5,1)
• (1,-5) and (5,-1)
• (1,-5)