Quadratic Basics
Graphing Quadratics
Solving Quadratics 1
Solving Quadratics 2
Solving Quadratics 3
100
The name given to the shape of a quadratic function
Parabola
100
Does the following quadratic equation have a maximum or a minimum?
y = -3x2 - 4x + 6
Maximum
100
Solve:
x2 - 16 = 9
x = ±5
100
Solve:
17 - 9x2 = 8
x = ±1
100
Solve: x2 - 16x + 63 = 0
x = 9 or x = 7
200
The name given to the maximum/minimum point of a quadratic function
Vertex
200
What is the vertex?
y = 1/2 (x - 4)2 - 3
(4, -3)
200
AKA the zeros of a quadratic function?
x-intercepts of the function
200
Given the following graph of y = -x2 - 4x - 3, find the solution to -x2 - 4x - 3 = 0.
x = -3 or x = -1
200
Solve: 6x2 - 19 = 5
x = ±2
300
The name given to the line that splits a quadratic function into a mirror image of itself
Axis of symmetry
300
What is the range?
y = -2(x - 1)2 - 3
(-∞, -3]
300
Solve by factoring: x2 - 15x = 34
x = 17 or x = -2
300
Solve by factoring: 2x2 - 5x - 3 = 0
x = -1/2 or x = 3
300
Solve: 2x2 + 3x - 1 = 0
x = 0.28 or x = -1.78
400
How you know an equation is a quadratic
Equation of degree two
400
What is the axis of symmetry?
y = x2 - 5x + 2
x = 2.5
400
Solve by using the quadratic formula: 4x2 + 3x - 8 = 0
x = 1.09 or x = -1.84
400
Solve by using the quadratic formula: x2 - 3x - 6 = -10
No solution
400
Solve: 1/4 x2 + 4x = 4
x = 0.94 or x = -16.94
500
How to find the axis of symmetry if a quadratic equation is in standard form
x = -b/2a
500
What is the vertex?
y = -2x2 + 8x - 1
(2, 7)
500
The roots of 2(x-5)(3x-7)
x = 5 or x = 7/3
500
Solve by completing the square (must show work):
3x2 + 9x - 12 = 0
x = 1 or x = -4
500
If the sides of a square are increased by 3 meters, the area is 64 m2. Find the length of the side of the original square.
5 meters