Make a table and graph each quadratic function. Use integers from -3 to 3 for inputs.
#4- y= -x2
#5- y=2x squared
#6- y= -8x squared
#7- y= x squared + 2
Make a table and a graph for each function. Use only positive values for x.
#10- y= 10/x
#11- y= 8/x
Write a quadratic function rule for the data in each table
#14- x (-10, -5, 0, 5, 10
y (80, 5, -20, 5, 80
#15- x (0, 1, 2, 3, 4)
y (0.-1, -4, -9, -16)
Make a table and a graph for each quadratic function
#21- y= 2x squared + 2x + 2
#22- y = x=x squared
Translate each relation by representing it as a table, as a graph, and as a function rule
#2- P = 5 . 3n
#3- Input is 0, 1, 2, 3
Output is 10, 18, 26, 34
#4-Question: When might it be more useful to use a graph rather than a function rule? A function rule rather than a graph?
Anyone out there that can help?
For #4, I will provide step-by-step instructions for each question:
#4- y= -x^2
To create a table, substitute values from -3 to 3 for x into the equation and calculate the corresponding y values:
x | y
-3 | -9
-2 | -4
-1 | -1
0 | 0
1 | -1
2 | -4
3 | -9
To create a graph, plot the points from the table on a Cartesian plane.
The graph is a downward-opening parabola.
#5- y=2x^2
To create a table, substitute values from -3 to 3 for x into the equation and calculate the corresponding y values:
x | y
-3 | 18
-2 | 8
-1 | 2
0 | 0
1 | 2
2 | 8
3 | 18
To create a graph, plot the points from the table on a Cartesian plane.
The graph is an upward-opening parabola.
#6- y= -8x^2
To create a table, substitute values from -3 to 3 for x into the equation and calculate the corresponding y values:
x | y
-3 | -72
-2 | -32
-1 | -8
0 | 0
1 | -8
2 | -32
3 | -72
To create a graph, plot the points from the table on a Cartesian plane.
The graph is a downward-opening parabola.
#7- y= x^2 + 2
To create a table, substitute values from -3 to 3 for x into the equation and calculate the corresponding y values:
x | y
-3 | 11
-2 | 6
-1 | 3
0 | 2
1 | 3
2 | 6
3 | 11
To create a graph, plot the points from the table on a Cartesian plane.
The graph is an upward-opening parabola.
#10- y= 10/x
To create a table, substitute positive values for x into the equation and calculate the corresponding y values:
x | y
1 | 10
2 | 5
3 | 3.33
...
To create a graph, plot the points from the table on a Cartesian plane.
The graph curves downwards as x increases.
#11- y= 8/x
To create a table, substitute positive values for x into the equation and calculate the corresponding y values:
x | y
1 | 8
2 | 4
3 | 2.67
...
To create a graph, plot the points from the table on a Cartesian plane.
The graph curves downwards as x increases.
#14- Given the table:
x | y
-10 | 80
-5 | 5
0 | -20
5 | 5
10 | 80
To find the quadratic function rule, we can use the values of x and y to form a system of equations and solve for the coefficients. Substituting x = -10 and y = 80 into the general quadratic function y = ax^2 + bx + c, we get:
80 = a(-10)^2 + b(-10) + c
Simplifying further:
80 = 100a - 10b + c
Using the same process for other x and y values, we form a system of equations:
Equation 1: 80 = 100a - 10b + c
Equation 2: 5 = 25a - 5b + c
Equation 3: -20 = 0a + 0b + c
Equation 4: 5 = 25a + 5b + c
Equation 5: 80 = 100a + 10b + c
Solving this system of equations yields: a = 1, b = 0, c = -20
Thus, the quadratic function rule for this data is y = x^2 - 20.
#15- Given the table:
x | y
0 | 0
1 | -1
2 | -4
3 | -9
4 | -16
We can observe that the y-values are equal to the negative square of the corresponding x-values. Thus, the quadratic function rule for this data is y = -x^2.
#21- y= 2x^2 + 2x + 2
To create a table, substitute values from -3 to 3 for x into the equation and calculate the corresponding y values:
x | y
-3 | 14
-2 | 6
-1 | 2
0 | 2
1 | 4
2 | 10
3 | 20
To create a graph, plot the points from the table on a Cartesian plane.
The graph is an upward-opening parabola.
#22- y = x^3
To create a table, substitute values from -3 to 3 for x into the equation and calculate the corresponding y values:
x | y
-3 | -27
-2 | -8
-1 | -1
0 | 0
1 | 1
2 | 8
3 | 27
To create a graph, plot the points from the table on a Cartesian plane.
The graph forms a curve but is not a quadratic function.
#2- P = 5 * 3n
To represent the relation as a table, substitute values from 0 to 3 for n into the equation and calculate the corresponding P values:
n | P
0 | 5
1 | 15
2 | 45
3 | 135
To represent the relation as a graph, plot the points from the table on a Cartesian plane. The graph will show the increasing values of P as n increases.
To represent the relation as a function rule, we can see that P is obtained by multiplying 5 with 3 raised to the power of n. Thus, the function rule is P = 5 * 3^n.
#3- Given the input and output values:
Input: 0, 1, 2, 3
Output: 10, 18, 26, 34
To represent the relation as a table, the input values correspond to the x-column and the output values correspond to the y-column:
x | y
0 | 10
1 | 18
2 | 26
3 | 34
To represent the relation as a graph, plot the points from the table on a Cartesian plane. The graph will show the increasing values of y as x increases.
To represent the relation as a function rule, we can see that y is obtained by multiplying the input x by 8 and adding 10. Thus, the function rule is y = 8x + 10.
Question #4: When might it be more useful to use a graph rather than a function rule? A function rule rather than a graph?
Using a graph can be more useful when we need to visualize the overall pattern or trend in a set of data points. It allows us to see the relationship between two variables and identify any specific patterns, such as increasing or decreasing trends, maximum or minimum values, or any irregularities.
On the other hand, using a function rule can be more useful when we need to determine specific values for a given input without having to plot and interpret a graph. It provides a clear and concise rule to calculate the output for any given input value within the defined domain of the function.
To make a table and graph for each quadratic function, we will substitute integers from -3 to 3 for the inputs.
#4- y = -x^2
Table:
x | y
---------------
-3 | -9
-2 | -4
-1 | -1
0 | 0
1 | -1
2 | -4
3 | -9
Graph:
|
* |
|
* |
|
* |
|
---------------
| |
-3 -2 ...
#5- y = 2x^2
Table:
x | y
---------------
-3 | 18
-2 | 8
-1 | 2
0 | 0
1 | 2
2 | 8
3 | 18
Graph:
|
|
* | *
|
---------------
| |
-3 -2 ...
#6- y = -8x^2
Table:
x | y
---------------
-3 | -72
-2 | -32
-1 | -8
0 | 0
1 | -8
2 | -32
3 | -72
Graph:
|
* |
|
* |
|
* |
|
---------------
| |
-3 -2 ...
#7- y = x^2 + 2
Table:
x | y
---------------
-3 | 11
-2 | 6
-1 | 3
0 | 2
1 | 3
2 | 6
3 | 11
Graph:
|
|
* | *
|
---------------
| |
-3 -2 ...
To write a quadratic function rule for the data in each table:
#14- x (-10, -5, 0, 5, 10)
y (80, 5, -20, 5, 80)
Based on the data, the pattern of the quadratic function seems to be a symmetric parabola with a vertex at (0, -20). The function rule can be written as y = x^2 - 20.
#15- x (0, 1, 2, 3, 4)
y (0, -1, -4, -9, -16)
Based on the data, the pattern of the quadratic function seems to be a downward-opening parabola. The function rule can be written as y = -x^2.
To make a table and graph for each quadratic function:
#21- y = 2x^2 + 2x + 2
Table:
x | y
---------------
-3 | 8
-2 | 2
-1 | 0
0 | 2
1 | 8
2 | 18
3 | 32
Graph:
|
* |
|
* |
|
* |
|
---------------
| |
-3 -2 ...
#22- y = x^2
Table:
x | y
---------------
-3 | 9
-2 | 4
-1 | 1
0 | 0
1 | 1
2 | 4
3 | 9
Graph:
|
|
* |
|
---------------
| |
-3 -2 ...
For the relations represented as tables, graphs, and function rules:
#2- P = 5 * 3n
Table:
n | P
---------------
0 | 0
1 | 15
2 | 30
3 | 45
Graph:
|
* |
|
* |
|
* |
|
---------------
| |
-3 -2 ...
Function rule: P = 5 * 3n
#3- Input: 0, 1, 2, 3
Output: 10, 18, 26, 34
Table:
Input (n) | Output (P)
---------------
0 | 10
1 | 18
2 | 26
3 | 34
Graph:
|
* |
|
* |
|
* |
|
---------------
| |
-3 -2 ...
Function rule: P = 8n + 10
If you need to represent a relationship between two variables and show how they vary with each other, a graph may be more useful. Graphs provide a visual representation that can help identify patterns, trends, and relationships between variables.
On the other hand, if you need to express the relationship between two variables using a specific mathematical equation or formula, a function rule may be more useful. Function rules provide a concise and precise way to express the relationship between variables using mathematical notation.
The choice between using a graph or a function rule depends on the specific context and purpose of the analysis or problem-solving process.