Factor the following to find solutions:
y = x^2 +2x - 24
x = -6 AND x = 4
100
How do you find the axis of symmetry of a graph from standard form? How about vertex form? Intercept form?
Standard: x = -B/2A
Vertex: x = h
Intercept: x = (p+q)/2
100
A rectangle is 5 feet longer than its width. Its area is 50 square feet. What are the dimensions of the rectangle?
5 ft. X 10 ft.
100
What is the quadratic formula?
x = (-B ± √(B^2 - 4AC)) / 2A
100
Is the axis of symmetry a function? Explain why or why not
No, does not pass vertical line test, undefined slope
200
Factor the following to find the solutions:
y = 64x^2 + 16x
x = 0 AND x = -1/4
200
Graph the following quadratic function:
y = x^2 + 4x - 12
Axis of Symmetry: x = -2
Vertex: (-2, -16)
X-Intercepts: (-6, 0) and (2,0)
200
The length of a rectangle is twice as long as it is wide. The area of this rectangle is 128 square feet. What are the dimensions of this rectangle?
8 feet X 16 feet
200
What is the expression underneath the radical sign in the quadratic formula called? What information does this give you?
The Discriminant
1. Real or Imaginary
2. Rational or Irrational
3. How many solutions?
200
What is the discriminant of the following quadratic?
y = -2x^2 - 3x + 12
What does this number tell you about the solutions?
105
1. Real Solutions
2. Irrational Solutions
3. Two Solutions
300
Factor the following to find solutions:
y = 5x^2 - 125
x = 5 AND x = -5
300
Graph the following quadratic function:
y = x^2 - 10x + 9
Axis of Symmetry: x = 5
Vertex: (5, -16)
X-Intercepts: (1,0) AND (9, 0)
300
A farmer builds a rectangular barn in the middle of one of his fields. The barn is 3 times longer than it is wide and it is surrounded by 3 feet of grass on all sides. If the area of the barn and the grass combined is 576 sq. feet, what are the dimensions of the barn?
10 feet X 30 feet
300
Use the quadratic formula to find solutions of the following quadratic:
y = x^2 + 11x + 10
x = -10 AND x = -1
300
Solve the following system of equations by any method of your choosing
3x - 2y = 2
5x - 5y = 10
(-2, -4)
400
Factor the following to find solutions:
y = 2x^2 + 6x -108
x = 6 AND x = -9
400
Graph the following quadratic function:
y = 5x^2 + 10x + 20
Axis of Symmetry: x = -1
Vertex: (-1, 15)
X-Intercepts: NONE
400
James is a contractor who has been given a rectangular plot of land on which to construct a rectangular building. There are only three stipulations to this project. First, the plot of land is twice as long as it is wide. Second, the building must be placed in the center of the plot so that a lawn with a uniform width of 2.5 feet surrounds the building on all sides. Finally, the area of the building must be 250 square feet. What are the dimensions of the building?
10 feet X 25 feet
400
Use quadratic formula to find solutions of the following quadratic:
y = x^2 - 14x + 49
x = 7
400
Find the solutions to the following quadratic:
2x^2 - 7x - 13 = -10
x = (7 + √73) / 4 AND x = (7 - √73) / 4
500
Factor the following to find solutions:
y = 4x^2 - 15x - 25
x = 5 AND x = -5/4
500
Graph the following quadratic function:
y = x^2 - 7x + 10
Axis of Symmetry: x = 7/2
Vertex: (7/2, -9/4)
X-Intercepts: (2,0) AND (5,0)
500
A rectangular garden is placed in the middle of a rectangular backyard. The garden is 4 feet longer than 4 times its width. A path of uniform width surrounds the garden. The total area of the backyard is 330 square feet. If the garden is 5 feet wide, how wide is the surrounding pathway?
3 feet
500
Use quadratic formula to find solutions of the following quadratic:
y = 6x^2 + 66x + 60
x = -1 AND x = -10
500
Find the equation of a quadratic function, in standard form, of a graph with intercepts at (-2,0) and (5,0) which crosses through the point (7,9)