make a table and graph each quadratic function. use integers from -3 to 3 inputs 1. y=-x^2 2. y=2x^2 3. y=-8x^2 4. x^2 + 2
To solve this, we need to substitute integer values from -3 to 3 into each quadratic function to get the corresponding output values. Then, we can create a table and graph for each function based on the calculated values.
1. y = -x^2:
Let's substitute the values of x from -3 to 3 into the equation and calculate the corresponding y values:
For x = -3, y = -(-3)^2 = -9
For x = -2, y = -(-2)^2 = -4
For x = -1, y = -(-1)^2 = -1
For x = 0, y = -(0)^2 = 0
For x = 1, y = -(1)^2 = -1
For x = 2, y = -(2)^2 = -4
For x = 3, y = -(3)^2 = -9
Now, we can create a table:
| x | y |
|---|---|
| -3| -9|
| -2| -4|
| -1| -1|
| 0| 0|
| 1| -1|
| 2| -4|
| 3| -9|
Next, let's plot the points on the graph:
```
(0, 0)
|
(-1, -1) (1, -1)
|
(-2, -4) (2, -4)
|
(3, -9)
```
2. y = 2x^2:
Similarly, we substitute the values of x from -3 to 3 into the equation to calculate the corresponding y values:
For x = -3, y = 2(-3)^2 = 18
For x = -2, y = 2(-2)^2 = 8
For x = -1, y = 2(-1)^2 = 2
For x = 0, y = 2(0)^2 = 0
For x = 1, y = 2(1)^2 = 2
For x = 2, y = 2(2)^2 = 8
For x = 3, y = 2(3)^2 = 18
Creating a table:
| x | y |
|---|---|
| -3| 18|
| -2| 8|
| -1| 2|
| 0| 0|
| 1| 2|
| 2| 8|
| 3| 18|
Plotting the points:
```
(0, 0)
|
(-1, 2) (1, 2)
|
(-2, 8) (2, 8)
|
(3, 18)
```
3. y = -8x^2:
Substituting values of x from -3 to 3 into the equation:
For x = -3, y = -8(-3)^2 = -72
For x = -2, y = -8(-2)^2 = -32
For x = -1, y = -8(-1)^2 = -8
For x = 0, y = -8(0)^2 = 0
For x = 1, y = -8(1)^2 = -8
For x = 2, y = -8(2)^2 = -32
For x = 3, y = -8(3)^2 = -72
Creating a table:
| x | y |
|---|-----|
| -3| -72 |
| -2| -32 |
| -1| -8 |
| 0| 0 |
| 1| -8 |
| 2| -32 |
| 3| -72 |
Plotting the points:
```
(0, 0)
|
(-1, -8) (1, -8)
|
(-2, -32) (2, -32)
|
(3, -72)
```
4. y = x^2 + 2:
Substituting values of x from -3 to 3 into the equation:
For x = -3, y = (-3)^2 + 2 = 11
For x = -2, y = (-2)^2 + 2 = 6
For x = -1, y = (-1)^2 + 2 = 3
For x = 0, y = (0)^2 + 2 = 2
For x = 1, y = (1)^2 + 2 = 3
For x = 2, y = (2)^2 + 2 = 6
For x = 3, y = (3)^2 + 2 = 11
Creating a table:
| x | y |
|---|----|
| -3| 11 |
| -2| 6 |
| -1| 3 |
| 0| 2 |
| 1| 3 |
| 2| 6 |
| 3| 11 |
Plotting the points:
```
(0, 2)
|
(-1, 3) (1, 3)
|
(-2, 6) (2, 6)
|
(3, 11)
```
That's it! You have created tables and graphs for each quadratic function using the given inputs.
Just do it.
The instructions are quite clear.