QuestionFind the intercepts of the equation $y=3x^{2}-3$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $y=3x^{}-3$ . We are asked to find the intercept(s) of the equation. There are two types of intercepts x-intercept(s) and y-intercept(s).
3. An x-intercept is a point where the graph of the equation crosses the x-axis. At these points, $y=0$ .
4. A y-intercept is a point where the graph of the equation crosses the y-axis. At these points, $x=0$ .

STEP 2

First, let's find the x-intercept(s) of the equation. We do this by setting $y=0$ and solving for $x$ .
$0=x^{2}-$

STEP 3

To solve for $x$ , we first add3 to both sides of the equation.
$3=3x^{2}$

STEP 4

Next, we divide both sides of the equation by3 to isolate $x^{2}$ .
$x^{2}=1$

STEP 5

Finally, we take the square root of both sides of the equation to solve for $x$ . Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x=\sqrt{1}, -\sqrt{1}$

STEP 6

Calculate the x-intercept(s).
$x=1, -1$

STEP 7

Now, let's find the y-intercept of the equation. We do this by setting $x=0$ and solving for $y$ .
$y=3(0)^{2}-3$

STEP 8

Calculate the y-intercept.
$y=-3$ The x-intercepts of the equation are $x=1$ and $x=-1$ , and the y-intercept of the equation is $y=-3$ .

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QuestionFind the intercepts of the equation $y=3x^{2}-3$ .

Studdy Solution

STEP 1

STEP 2

First, let's find the x-intercept(s) of the equation. We do this by setting $y=0$ and solving for $x$ .
$0=x^{2}-$

STEP 3

To solve for $x$ , we first add3 to both sides of the equation.
$3=3x^{2}$

STEP 4

Next, we divide both sides of the equation by3 to isolate $x^{2}$ .
$x^{2}=1$

STEP 5

Finally, we take the square root of both sides of the equation to solve for $x$ . Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x=\sqrt{1}, -\sqrt{1}$

STEP 6

Calculate the x-intercept(s).
$x=1, -1$

STEP 7

Now, let's find the y-intercept of the equation. We do this by setting $x=0$ and solving for $y$ .
$y=3(0)^{2}-3$

STEP 8

Calculate the y-intercept.
$y=-3$ The x-intercepts of the equation are $x=1$ and $x=-1$ , and the y-intercept of the equation is $y=-3$ .

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QuestionFind the intercepts of the equation y=3x2−3y=3x^{2}-3y=3x2−3.

Studdy Solution

STEP 1

STEP 2

First, let's find the x-intercept(s) of the equation. We do this by setting y=0y=0y=0 and solving for xxx.0=x2−0=x^{2}-0=x2−

STEP 3

To solve for xxx, we first add3 to both sides of the equation.3=3x23=3x^{2}3=3x2

STEP 4

Next, we divide both sides of the equation by3 to isolate x2x^{2}x2.x2=1x^{2}=1x2=1

STEP 5

Finally, we take the square root of both sides of the equation to solve for xxx. Remember, when we take the square root of a number, we get two solutions one positive and one negative.x=1,−1x=\sqrt{1}, -\sqrt{1}x=1​,−1​

STEP 6

Calculate the x-intercept(s).x=1,−1x=1, -1x=1,−1

STEP 7

Now, let's find the y-intercept of the equation. We do this by setting x=0x=0x=0 and solving for yyy.y=3(0)2−3y=3(0)^{2}-3y=3(0)2−3

STEP 8

Calculate the y-intercept.y=−3y=-3y=−3The x-intercepts of the equation are x=1x=1x=1 and x=−1x=-1x=−1, and the y-intercept of the equation is y=−3y=-3y=−3.

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QuestionFind the intercepts of the equation $y=3x^{2}-3$ .

First, let's find the x-intercept(s) of the equation. We do this by setting $y=0$ and solving for $x$ .
$0=x^{2}-$

To solve for $x$ , we first add3 to both sides of the equation.
$3=3x^{2}$

Next, we divide both sides of the equation by3 to isolate $x^{2}$ .
$x^{2}=1$

Finally, we take the square root of both sides of the equation to solve for $x$ . Remember, when we take the square root of a number, we get two solutions one positive and one negative.
$x=\sqrt{1}, -\sqrt{1}$

Calculate the x-intercept(s).
$x=1, -1$

Now, let's find the y-intercept of the equation. We do this by setting $x=0$ and solving for $y$ .
$y=3(0)^{2}-3$

Calculate the y-intercept.
$y=-3$ The x-intercepts of the equation are $x=1$ and $x=-1$ , and the y-intercept of the equation is $y=-3$ .