INVESTIGATION I.
I. Graph the function 𝑦 = 𝑥 2 in a Cartesian plane using table of values
II. For each quadratic function below, you and your partner will describe the changes
on the parent function 𝑦 = 𝑥 2 into the given quadratic function. Use the DESMOS
app in your Ipad.
1.
Given the following functions, compare and describe what happened to each
graph compared to the parent function
a) 𝑦 = −𝑥 2
It went to the opossite direction but it had the same size
_________________________________________________
b)𝑦 = 4𝑥 2
The
line got thinner thatn y=x squared
_________________________________________________
c) 𝑦 = −4𝑥 2
It was the exact same size but in the different direction
_________________________________________________
d) Without graphing, describe what kind of graph 𝑦 = −10𝑥 2 and
𝑦 = 10𝑥 2 will have.
It will look exactly the same but facing each other opening up to different directions
____________________________________________________
2.
Given the following functions, compare and describe what happened to each
graph compared to the parent function
a) 𝑦 = 25𝑥 2
The concavity got a little bigger
_________________________________________________
b) 𝑦 = 100𝑥 2
The concavity got thinner than a
_________________________________________________
1
c) 𝑦 = 𝑥 2
2
The concavity is bigger than a
_________________________________________________
d) 𝑦 =
1
10
𝑥2
It had the biggest concavity
_________________________________________________
1
3. Without graphing, describe what kind of graph 𝑦 = 5𝑥 2 and 𝑦 = 𝑥 2 will
5
have and compare them to the graph of the parent function.
__________________________________________________________
The first function will have a smaller concavity than the parent function while the second function will have a
larger concavity.
4. The role of a in the graph of the function 𝑦 = 𝑎𝑥 2 is
It determines how big or small the concavity of the line will be
__________________________________________________________
III. Refer to the graph of the parent function 𝑦 = 𝑥 2 in answering the items below.
Use the DESMOS app in your iPad.
a. How would the graph of 𝑦 = 𝑥 2 + 8 appear? What about the graph of
𝑦 = 𝑥 2 + 12?
What do you notice about the graph of the new functions?
______________________________________
The first function’s graph is higher on the y axis compared to the second
one and the higher the constant is the higher the vertex is in the y axis
b. Without graphing, describe what kind of graph 𝑦 = 𝑥 2 + 15 and
The first function will start on a lower
𝑦 = 𝑥 2 + 80 will have.
y axis number compared to the
second one
__________________________________________________________
c. How would the graph of 𝑦 = 𝑥 2 − 5 appear? What about the graph of
𝑦 = 𝑥 2 − 15?
What do you notice about the graph of the new functions?
It will face upwards but the first function will start higher in the graph compared to the second
______________________________________
d. Without graphing, describe what kind of graph 𝑦 = 𝑥 2 − 9 and
𝑦 = 𝑥 2 − 24 will have.
They will both face upwards but the first function will start higher on the y axis and nearer to 0
__________________________________________________________
The role of k in the graph of the function 𝑦 = 𝑥 2 + 𝑘 is
The role of k is the vertex
__________________________________________________________
___________________________
IV. Refer to the graph of the parent function 𝑦 = 𝑥 2 in answering the items below.
Use the DESMOS app in your iPad.
a. How would the graph of 𝑦 = (𝑥 − 3)2 appear? What about the graph
of 𝑦 = (𝑥 + 7)2 ?
What do you notice about the graph of the new functions?
The first
function’s graph’s vertex is closer to 0 in the x axis compared to the 2nd function
______________________________________
b. What can you say about the graph of 𝑦 = (𝑥 − 4)2 and 𝑦 = (𝑥 + 3)2 ?
The first function is found on the positive side of the horizontal axis while the 2nd was found on the negative part
c. Without graphing, describe what kind of graph 𝑦 = (𝑥 − 13)2 and
𝑦 = (𝑥 + 24)2 will have
__________________________________________________________
d. The role of h in the graph of the function 𝑦 = (𝑥 − ℎ)2
__________________________________________________________
V. Consider the function 𝑦 = 2(𝑥 − 3)2 + 6. What changes will it have from the
graph of the parent function y = x2?
VI. Consider the function 𝑦 =
−1
3
(𝑥 + 5)2 − 2. What transformations will it have
from the graph of the parent function?