What does this formula do?
Find the vertex
Find the domain/range
What does the graph look like?
What does the equation look like?
100
What does k do in: g(x) = x2 + k
The value of k translates the graph vertically (up and down)
100
Find the vertex of
y = (x - 3)2
Vertex is at (3, 0)
100
Find the domain and range of
y = (x - 4)2
Domain is at all real numbers
Range is y >= 0
100
Draw the graph of:
f(x) = x2+3
Answer #1
100
Find f(x)
f(x) = x2
200
What does h do in: g(x) = (x - h)2
The value of h translates the graph horizontally (left to right)
200
Find the vertex of
f(x) = x2 + 27
Vertex is at (0, 27)
200
Find the domain and range of
g(x) = x2 + 7
Domain is at all real numbers
Range is y >= 7
200
Draw the graph of
g(x) = -(x + 2)2
Answer #2
200
Vertex is at (0, 4)
Axis of symmetry is at x = 0
Vertical stretch of 4
Graph opens down
Range is y <= 4
f(x) = -4x2 + 4
300
What does h and k do in: f(x)= +/- (x - h)2 + k
h and k determine the location of the vertex and the axis of symmetry
300
Find the vertex of
g(x) = -(x+6)2 - 6
Vertex is at (-6, -6)
300
Find the domain at range of
y = - (x + 3)2 - 2
Domain is at all real numbers
Range is y <= -2
300
Draw the graph of
h(x) = (x - 4)2 +2
Answer #3
300
Vertex is at (5, -3)
Axis of symmetry is at x = 5
Vertical stretch of 1/3
Graph opens up (Range is at y >= -3)
f(x) = 1/3 (x - 5)2 - 3
400
What happens to the graph when there is a negative in front of the equation? Ex: - (x -h)2, -x2 + k
The graph opens down instead of up
400
Find the vertex of
y = x2 - 7/3
Vertex is at (0, -7/3)
400
Find the domain and range of
y = (x - 7)2 - 4/3
Domain is at all real numbers
Range is at y >= -4/3
400
Draw the graph of (x - 9/2)2 + 7/2
Answer #4
400
Vertex at (2, 2)
Vertical stretch of 3
Axis of symmetry at x = 2
Parabola opens up
y = 3 (x - 2)2 + 2
500
What does the graph look like when there is a whole number in front of it? Ex: 2(x - h)2 + k , 6x2
The graph becomes more narrow (skinny)
500
Find the vertex of (x + 5/2)2 + 3
Vertex is at (-5/2, 3)
500
Find the domain and range of
y = -(x + 9/2)2 + 3
Domain is at all real numbers
Range is at y <= 3
500
Draw the graph of y = -2x2
Answer #5
500
Vertex at (-7, 3)
Axis of symmetry at x = 7
Vertical shrink of 1/2
Range is y <= 3
y = -1/2 (x + 7)2 + 3