MFM 2P:
OBSERVATIONS ABOUT PARABOLAS
Name: _____________________________ Date: _____________________________
Goal: By looking at the graphs and the equations of parabolas I will be able to
determine the vertex and the direction of the opening.
Go to this website: https://www.desmos.com/calculator
Enter the equations and look at the graphs. Record information about the parabola.
Graph the parabolas by groups of 4 on the grid, make observations about the group,
clear the equations and start on the next group.
GROUP 1:
Equation
Vertex (x,y)
Direction of opening
𝑦 = 𝑥2
𝑦 = (𝑥 − 1)2
𝑦 = (𝑥 − 4)2
𝑦 = (𝑥 + 5)2
Observations:
What is the same about this group of parabolas?
Axis of Symmetry
What is different about this group of parabolas?
GROUP 2:
Equation
Vertex (x,y)
Direction of opening
𝑦 = 𝑥2
𝑦 = 𝑥2 + 4
𝑦 = 𝑥2 − 5
𝑦 = 𝑥2 − 2
Observations:
What is the same about this group of parabolas?
Axis of Symmetry
What is different about this group of parabolas?
GROUP 3:
Equation
Vertex (x,y)
Direction of opening
2
𝑦 = −2𝑥
𝑦 = −4(𝑥 − 1)2
𝑦 = −0.5(𝑥 − 4)2
𝑦 = −6(𝑥 + 5)2
Observations:
What is the same about this group of parabolas?
What is different about this group of parabolas?
Axis of Symmetry
GROUP 4:
Equation
Vertex (x,y)
Direction of opening
2
𝑦=𝑥
𝑦 = (𝑥 − 1)2 +3
𝑦 = (𝑥 − 4)2 -4
𝑦 = (𝑥 + 5)2 − 2
Observations:
What is the same about this group of parabolas?
Axis of Symmetry
What is different about this group of parabolas?
GROUP 5:
Equation
Vertex (x,y)
Direction of opening
𝑦 = −2𝑥 2
𝑦 = −3(𝑥 + 1)2 +3
𝑦 = −0.5(𝑥 − 4)2 -4
𝑦 = −2(𝑥 + 5)2 − 2
Observations:
What is the same about this group of parabolas?
Axis of Symmetry
What is different about this group of parabolas?
GROUP 6:
Equation
Vertex (x,y)
Direction of opening
𝑦 = 𝑥2
𝑦 = −3(𝑥 − 1)2 + 2
𝑦 = 2(𝑥 − 2)2 -4
𝑦 = −3(𝑥 − 6)2 − 3
Observations:
What is the same about this group of parabolas?
Axis of Symmetry
What is different about this group of parabolas?
Generalizing my observations:
𝒚 = ±𝒂(𝒙 − 𝒉)𝟐 + 𝒌
What did you notice about all parabolas that opened up?
What did you notice about all parabolas that opened down?
What did you notice about the vertex and the numbers in the equations?
What did you notice about the axis of symmetry?