Quadratic Models Investigations
Investigation – The curve y = ax2
1. Graph these curves on your GDC: y= x2 and y= -x2
How are these two curves related? ______________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2. Now graph and compare each of these six graphs to y=x2:
y = 2x2, y = 3x2, y = 0.5x2
y = -2x2, y = -3x2, y = -0.5x2
Equation
Is the curve still a
parabola? Is the curve
- shaped or shaped?
Does it have a vertical
line of symmetry?
What is its vertex? Is
the vertex a minimum
or maximum point?
y = 2x2
y = 3x2
y = 0.5x2
y = -2x2
y = -3x2
y = -0.5x2
What is the effect of changing the value of a? ______________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
3. Graph three more equations on your GDC to test your conjecture. (Remember to use positives
and negatives of a and also use fractions.)
List the graphs you tested: __________, __________, and __________
Investigation – The curve y=x2+ c
1. Graph these curves on your GDC and compare each of these six graphs to y= x2:
y= x2,
Equation
y= x2+ 2,
y= x2- 4, y= x2+ 3, y= x2- 2
Is the curve still a
parabola? Is the curve
- shaped or shaped?
Does it have a vertical
line of symmetry?
What is its vertex? Is
the vertex a minimum
or maximum point?
y=x2
y=x2+2
y=x2- 4
y=x2+ 3
y=x2- 2
What is the effect of changing the value of c? ______________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2. Graph three more equations on your GDC to test your conjecture. (Remember to use positives
and negatives of c)
List the graphs you tested: __________, __________, and __________
Practice: Use your results from the two previous investigations to help you sketch these graphs.
1. y = 2x2 + 1
2. y = -x2 + 3
3. y = 3x2 – 2
2
4. y = -2x2+ 7
Investigation – The curves y = (x + p)2 and y = (x + p)2+ q
1. Use your GDC to draw these graphs and compare each graph to the graph of y=x2:
y = x2, y = (x+2)2, y = (x+3)2, y = (x-1)2, y = (x- 0.5)2
What is the effect of changing the value of p? _________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2. Use your GDC to draw these graphs:
y = (x+2)2 - 3, y = (x-4)2 + 2, y = (x-1)2- 5
Equation
What is the axis of
symmetry of
y=(x+p)2 + q?
What are the
coordinates of the
vertex of y=(x+p)2+q?
y = (x+2)2 – 3
y = (x-4)2 + 2
y = (x-1)2- 5
Practice: For each graph, write down the coordinates of the vertex and the axis of symmetry.
1. y = (x+3)2 – 2
Vertex: ( _____, _____ )
Axis of Symmetry: _____________
Vertex: ( _____, _____ )
Axis of Symmetry: _____________
Vertex: ( _____, _____ )
Axis of Symmetry: _____________
Vertex: ( _____, _____ )
Axis of Symmetry: _____________
Vertex: ( _____, _____ )
Axis of Symmetry: _____________
2. y = (x+5)2 + 4
3. y = (x-4)2 – 1
4. y = (x-5)2 + 7
5. y = -(x+3)2 + 4
3