Convert Y = 3x^2 To Standard Form In 5 Steps

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Converting a quadratic equation from vertex form to standard form can be a bit tricky, but with the right steps, you'll be able to do it with ease. In this article, we'll take the equation Y = 3x^2 and convert it to standard form in 5 simple steps.

The importance of converting equations to standard form cannot be overstated. Standard form makes it easier to compare and analyze different equations, and it's a crucial step in solving quadratic equations. So, let's dive in and learn how to convert Y = 3x^2 to standard form.

Step 1: Identify the Vertex Form

The given equation is Y = 3x^2, which is in vertex form. The vertex form of a quadratic equation is Y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, we can see that a = 3, h = 0, and k = 0.

Understanding the Vertex Form

The vertex form is useful for identifying the vertex of the parabola, but it's not the most convenient form for solving quadratic equations. That's why we need to convert it to standard form.

Step 2: Expand the Equation

To convert the equation to standard form, we need to expand the squared term. We can do this by multiplying the term (x - 0) by itself.

Y = 3(x - 0)^2 Y = 3(x^2 - 2(0)x + 0^2) Y = 3(x^2 - 0x + 0) Y = 3x^2 - 0x + 0

Simplifying the Equation

Now that we've expanded the equation, we can simplify it by combining like terms. In this case, the equation simplifies to Y = 3x^2.

Step 3: Rearrange the Terms

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. To convert our equation to standard form, we need to rearrange the terms so that they match this format.

Y = 3x^2 3x^2 = Y 3x^2 - Y = 0

Matching the Standard Form

Now that we've rearranged the terms, we can see that our equation matches the standard form. The coefficient of x^2 is 3, the coefficient of x is 0, and the constant term is 0.

Step 4: Write the Standard Form

Now that we've rearranged the terms, we can write the equation in standard form.

3x^2 - Y = 0

Finalizing the Standard Form

We've successfully converted the equation Y = 3x^2 to standard form. The standard form is 3x^2 - Y = 0.

Step 5: Verify the Standard Form

Finally, let's verify that our equation is in standard form by checking that it matches the format ax^2 + bx + c = 0.

3x^2 - Y = 0

This equation matches the standard form, so we've successfully converted Y = 3x^2 to standard form.

Converting a quadratic equation from vertex form to standard form requires a few simple steps. By following these steps, you can convert any quadratic equation to standard form. Remember to expand the squared term, simplify the equation, rearrange the terms, write the standard form, and verify the standard form.

We hope this article has helped you learn how to convert Y = 3x^2 to standard form. If you have any questions or need further clarification, please don't hesitate to ask.