Question Find 7 points on the graph of $y=x^{2}$ , then determine the graph.

Studdy Solution

STEP 1

Assumptions
1. We are looking for ordered pairs that satisfy the equation $y=x^{2}$ .
2. The first value in each pair is the $x$ -value, and the second value is the $y$ -value.

STEP 2

The equation $y=x^{2}$ means that for any $x$ -value, the corresponding $y$ -value is the square of that $x$ -value. So, we can find the $y$ -values by squaring the $x$ -values.

STEP 3

Let's start with the given $x$ -value of -3. To find the corresponding $y$ -value, we square -3.
$y=(-3)^{2}$

STEP 4

Calculate the $y$ -value.
$y=(-3)^{2}=9$
So, the ordered pair for $x=-3$ is (-3, 9).

STEP 5

Now, let's find six more ordered pairs. We can choose any $x$ -values we want, but for simplicity, let's choose -2, -1, 0, 1, 2, and 3.

STEP 6

Calculate the $y$ -values for these $x$ -values using the equation $y=x^{2}$ .
For $x=-2$ :
$y=(-2)^{2}=4$
So, the ordered pair for $x=-2$ is (-2, 4).

STEP 7

For $x=-1$ :
$y=(-1)^{2}=1$
So, the ordered pair for $x=-1$ is (-1, 1).

STEP 8

For $x=0$ :
$y=(0)^{2}=0$
So, the ordered pair for $x=0$ is (0, 0).

STEP 9

For $x=1$ :
$y=(1)^{2}=1$
So, the ordered pair for $x=1$ is (1, 1).

STEP 10

For $x=2$ :
$y=(2)^{2}=4$
So, the ordered pair for $x=2$ is (2, 4).

STEP 11

For $x=3$ :
$y=(3)^{2}=9$
So, the ordered pair for $x=3$ is (3, 9).

STEP 12

Now, we have seven ordered pairs that satisfy the equation $y=x^{2}$ :
(-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9)

STEP 13

To graph these ordered pairs, we plot each pair as a point on a coordinate plane. The $x$ -value is the horizontal coordinate and the $y$ -value is the vertical coordinate.

STEP 14

After plotting these points, we can see that they form a curve that opens upwards. This is the graph of the equation $y=x^{2}$ .

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Question Find 7 points on the graph of $y=x^{2}$ , then determine the graph.

Studdy Solution

STEP 1

Assumptions
1. We are looking for ordered pairs that satisfy the equation $y=x^{2}$ .
2. The first value in each pair is the $x$ -value, and the second value is the $y$ -value.

STEP 2

The equation $y=x^{2}$ means that for any $x$ -value, the corresponding $y$ -value is the square of that $x$ -value. So, we can find the $y$ -values by squaring the $x$ -values.

STEP 3

Let's start with the given $x$ -value of -3. To find the corresponding $y$ -value, we square -3.
$y=(-3)^{2}$

STEP 4

Calculate the $y$ -value.
$y=(-3)^{2}=9$
So, the ordered pair for $x=-3$ is (-3, 9).

STEP 5

Now, let's find six more ordered pairs. We can choose any $x$ -values we want, but for simplicity, let's choose -2, -1, 0, 1, 2, and 3.

STEP 6

Calculate the $y$ -values for these $x$ -values using the equation $y=x^{2}$ .
For $x=-2$ :
$y=(-2)^{2}=4$
So, the ordered pair for $x=-2$ is (-2, 4).

STEP 7

For $x=-1$ :
$y=(-1)^{2}=1$
So, the ordered pair for $x=-1$ is (-1, 1).

STEP 8

For $x=0$ :
$y=(0)^{2}=0$
So, the ordered pair for $x=0$ is (0, 0).

STEP 9

For $x=1$ :
$y=(1)^{2}=1$
So, the ordered pair for $x=1$ is (1, 1).

STEP 10

For $x=2$ :
$y=(2)^{2}=4$
So, the ordered pair for $x=2$ is (2, 4).

STEP 11

For $x=3$ :
$y=(3)^{2}=9$
So, the ordered pair for $x=3$ is (3, 9).

STEP 12

Now, we have seven ordered pairs that satisfy the equation $y=x^{2}$ :
(-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9)

STEP 13

To graph these ordered pairs, we plot each pair as a point on a coordinate plane. The $x$ -value is the horizontal coordinate and the $y$ -value is the vertical coordinate.

STEP 14

After plotting these points, we can see that they form a curve that opens upwards. This is the graph of the equation $y=x^{2}$ .

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Question Find 7 points on the graph of y=x2y=x^{2}y=x2, then determine the graph.

Studdy Solution

STEP 1

Assumptions1. We are looking for ordered pairs that satisfy the equation y=x2y=x^{2}y=x2.2. The first value in each pair is the xxx-value, and the second value is the yyy-value.

STEP 2

The equation y=x2y=x^{2}y=x2 means that for any xxx-value, the corresponding yyy-value is the square of that xxx-value. So, we can find the yyy-values by squaring the xxx-values.

STEP 3

Let's start with the given xxx-value of -3. To find the corresponding yyy-value, we square -3.y=(−3)2y=(-3)^{2}y=(−3)2

STEP 4

Calculate the yyy-value.y=(−3)2=9y=(-3)^{2}=9y=(−3)2=9So, the ordered pair for x=−3x=-3x=−3 is (-3, 9).

STEP 5

Now, let's find six more ordered pairs. We can choose any xxx-values we want, but for simplicity, let's choose -2, -1, 0, 1, 2, and 3.

STEP 6

Calculate the yyy-values for these xxx-values using the equation y=x2y=x^{2}y=x2.For x=−2x=-2x=−2:y=(−2)2=4y=(-2)^{2}=4y=(−2)2=4So, the ordered pair for x=−2x=-2x=−2 is (-2, 4).

STEP 7

For x=−1x=-1x=−1:y=(−1)2=1y=(-1)^{2}=1y=(−1)2=1So, the ordered pair for x=−1x=-1x=−1 is (-1, 1).

STEP 8

For x=0x=0x=0:y=(0)2=0y=(0)^{2}=0y=(0)2=0So, the ordered pair for x=0x=0x=0 is (0, 0).

STEP 9

For x=1x=1x=1:y=(1)2=1y=(1)^{2}=1y=(1)2=1So, the ordered pair for x=1x=1x=1 is (1, 1).

STEP 10

For x=2x=2x=2:y=(2)2=4y=(2)^{2}=4y=(2)2=4So, the ordered pair for x=2x=2x=2 is (2, 4).

STEP 11

For x=3x=3x=3:y=(3)2=9y=(3)^{2}=9y=(3)2=9So, the ordered pair for x=3x=3x=3 is (3, 9).

STEP 12

Now, we have seven ordered pairs that satisfy the equation y=x2y=x^{2}y=x2:(-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9)

STEP 13

To graph these ordered pairs, we plot each pair as a point on a coordinate plane. The xxx-value is the horizontal coordinate and the yyy-value is the vertical coordinate.

STEP 14

After plotting these points, we can see that they form a curve that opens upwards. This is the graph of the equation y=x2y=x^{2}y=x2.

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Question Find 7 points on the graph of $y=x^{2}$ , then determine the graph.

Assumptions
1. We are looking for ordered pairs that satisfy the equation $y=x^{2}$ .
2. The first value in each pair is the $x$ -value, and the second value is the $y$ -value.

The equation $y=x^{2}$ means that for any $x$ -value, the corresponding $y$ -value is the square of that $x$ -value. So, we can find the $y$ -values by squaring the $x$ -values.

Let's start with the given $x$ -value of -3. To find the corresponding $y$ -value, we square -3.
$y=(-3)^{2}$

Calculate the $y$ -value.
$y=(-3)^{2}=9$
So, the ordered pair for $x=-3$ is (-3, 9).

Now, let's find six more ordered pairs. We can choose any $x$ -values we want, but for simplicity, let's choose -2, -1, 0, 1, 2, and 3.

Calculate the $y$ -values for these $x$ -values using the equation $y=x^{2}$ .
For $x=-2$ :
$y=(-2)^{2}=4$
So, the ordered pair for $x=-2$ is (-2, 4).

For $x=-1$ :
$y=(-1)^{2}=1$
So, the ordered pair for $x=-1$ is (-1, 1).

For $x=0$ :
$y=(0)^{2}=0$
So, the ordered pair for $x=0$ is (0, 0).

For $x=1$ :
$y=(1)^{2}=1$
So, the ordered pair for $x=1$ is (1, 1).

For $x=2$ :
$y=(2)^{2}=4$
So, the ordered pair for $x=2$ is (2, 4).

For $x=3$ :
$y=(3)^{2}=9$
So, the ordered pair for $x=3$ is (3, 9).

Now, we have seven ordered pairs that satisfy the equation $y=x^{2}$ :
(-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9)

To graph these ordered pairs, we plot each pair as a point on a coordinate plane. The $x$ -value is the horizontal coordinate and the $y$ -value is the vertical coordinate.

After plotting these points, we can see that they form a curve that opens upwards. This is the graph of the equation $y=x^{2}$ .