Finding the Vertex
What is the vertex of the following equation:
2(x-3)2+5
(3, 5)
Describe the transformations of the following equation:
(Does it shift left or right? up or down? stretch or compression? reflect?)
What is the axis of symmetry? (Remember it is the x-value of the vertex)
2(x-3)2+5
Stretch by 2, shift right by 3, shift up by 5
Axis of symmetry: x=3
Find the discriminant and state how many solutions this quadratic equation has.
x2-4x-5=0
36; 2 solutions
Find the solutions to the equation by using the quadratic formula
2x2-4x-6
x=3, x = -1
Solve by elimination.
x-y=11
2x+y=19
x = 10, y =-1
What is the vertex of the following equation:
(x-1)2-9
(1,-9)
Describe the transformations of the following equation:
(Does it shift left or right? up or down? stretch or compression? reflect?)
What is the axis of symmetry?
-0.5(x+2)2+2
Reflect, Compression by 0.5, shift left by 2, shift down by 2
Axis of symmetry: x=-2
Find the discriminant and state how many solutions this quadratic equation has.
x2+6x+9=0
0; 1 solution
Find the solutions to the equation by using the quadratic formula
x2+4x-5
x=1, x= -5
Solve by elimination.
-6x+5y=1
6x+4y=-10
x = -1, y= -1
What is the vertex of the following equation:
-3(x+2)2-4
(-2, -4)
Describe the transformations of the following equation:
(Does it shift left or right? up or down? stretch or compression? reflect?)
What is the axis of symmetry?
-(x-9)2-15
Reflect, shift right by 9, shift down by 15
Axis of symmetry: x = 9
Find the discriminant and state how many solutions this quadratic equation has.
2x2+8x+10=0
-16; No Solution
Find the solutions to the equation by using the quadratic formula
3x2+6x+2=0
x = 0.2440 and x = -0.9106
Solve by elimination.
8x+y=-16
-3x+y=-5
x=-1, y=-8
What is the vertex of the following equation:
-0.5(x+4)2+7
(-4, 7)
- Describe the transformations of the following equation.
- State the axis of symmetry.
- Graph the equation and:
1. state whether the vertex is a maximum or minimum
2. give the solution(s) (remember, this is a point where the graph crosses the x-axis).
(x+6)2-1
Shift left by 6, down by 1
Axis of symmetry: x = -6
Vertex is (-6,-1) and it's a minimum.
Solutions are x = -5, and x = -7
Find the discriminant and state how many solutions this quadratic equation has.
5x2-2x+7=0
-136; No solution
Find the solutions to the equation by using the quadratic formula
4x2+8x+3=0
x = -1/2 and x=-3/2
Solve by elimination.
5x+y=9
10x-7y=-18
x=1, y=4