The given equation is:

$y = 4x^2$

Step 1: Check if it represents a parabola

An equation represents a parabola if it is in the form:

$y = ax^2 + bx + c \quad \text{or} \quad x = ay^2 + by + c$

Here, $y = 4x^2$ matches the form $y = ax^2 + bx + c$, with $a = 4$, $b = 0$, and $c = 0$. Therefore, it does represent a parabola.

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Step 2: Rewrite in standard form

The standard form of a parabola (when it opens vertically) is:

$y - k = a(x - h)^2$

Here:

• $h = 0$, $k = 0$, and $a = 4$.

Thus, the equation in standard form is:

$y = 4(x - 0)^2 + 0 \quad \text{or simply} \quad y = 4x^2$

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Final Answer:

The equation represents a parabola, and it is already in standard form:

$y = 4x^2$

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Do you want details or have any questions?

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1. What are the key characteristics of a parabola based on its equation?
2. How can you identify the vertex of a parabola from its standard form?
3. What determines the direction of opening of a parabola?
4. How does the coefficient $a$ affect the shape of the parabola?
5. Can a parabola ever represent a horizontal line?

Tip: Always compare the given equation to the general forms of parabolas to quickly identify their characteristics.