Solve by Reasoning
Zero Product Property
Solutions From a Graph
Quadratic Context
Mixed Solving
100
Solve: x2=169
x=13 and x= -13
100
Solve for x: (x-1)(x+8)=0
x=1 and x= -8
100
f(x)=x2+3x-4 is graphed. What are the solution(s) to the equation: x2+3x-4=0
x=1 and x=-4
100
A 4x6 photo is being framed using 8 square inches of framing material. All of the framing material is to be used and the frame needs to have an equal width all the way around. The equation below can be solved to find x. What does x represent?
(4+2x)(6+2x)=32
The width of the frame.
100
x2-7x= -10
x=5 and x=2
200
Solve: x2+10=35
x=5 and x= -5
200
Solve for x: x(x-1)=0
x=0 and x=1
200
f(x)=x2-2x+1 is graphed. What are the solution(s) to the equation: x2-2x+1=0
x=1
200
A 5x7 inch photo is being framed with 12 square inches of framing material. All of the material is to be used and the frame needs to have an equal width all the way around. Fill in the missing part of the equation that could be solved to find the width of the framing material.
(5+2x)(7+2x)= ______
47
200
(x+4)2-2=79
x=5 and x= -13
300
Solve: (x-2)2=144
x=14 and x= -10
300
Solve for x: (x+3)(2x-5)=0
x= -3 and x= 5/2 or 2.5
300
f(x)=x2+4x+5 is graphed. What are the solution(s) to the equation: x2+4x+5=0
No Real Solutions
300
An 8x10 inch photo is being framed with 20 square inches of framing material. All of the framing material needs to be used and the frame needs to have an equal width all the way around. Write an equation that could be used to solve to determine the width of the frame, x.
(8+2x)(10+2x)=100
300
9x2-25=0
x=5/3 and x= -5/3
400
Solve: 5x2-15=5
x=2 and x= -2
400
Solve for x: x2+9x=0
x=0 and x= -9
400
f(x)= -x2+4x+5 is graphed. What are the solution(s) to the equation: -x2+4x= -5
x= -1 and x=5
400
A band is traveling to a new city to perform a concert. The revenue (amount of money brought in) from their ticket sales is a function of ticket price, x, and can be modeled with f(x)=(x-6)(250-5x). What are the ticket prices at which the band would make $0.
$6.00 and $50.00
400
3x2-18x-3= -10x
x=3 and x= -1/3
500
Solve: 2(x-1)2+3=101
x=8 and x= -6
500
Solve for x: x2+3x+2=0
x= -2 and x=1
500
f(x)=x2-2x+5 is graphed. What are the solution(s) to the equation: x2-2x+5=4
x=1
500
A rancher is making a square pen to enclose his goats. He needs the goats to have 324 square feet of space to roam.
Write the equation that could be used to find the side length of the square pen.
Solve your equation and include units in your response.
x2=324
x=18 feet
500
5x2+5x-3= -8x-9
x= -2 and x= -0.6