Find the equation of the parabola under the condition given below: vertex is at the origin and passing through (-1,4)

Given that the vertex of the parabola is at the origin \((0, 0)\) and the parabola passes through the point \((-1, 4)\), we can determine the equation of the parabola.

For a parabola with its vertex at the origin, the general equation is:

\[
y = ax^2
\]

Since the parabola passes through the point \((-1, 4)\), we can substitute these coordinates into the equation to find the value of \(a\).

\[
4 = a(-1)^2
\]

\[
4 = a(1)
\]

\[
a = 4
\]

Therefore, the equation of the parabola is:

\[
y = 4x^2
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What is the focus of the parabola \(y = 4x^2\)?
2. How would the equation change if the parabola opened downwards?
3. Can you determine the equation of a parabola with a different vertex?
4. What are the properties of parabolas that have vertical axes of symmetry?
5. How would you find the directrix of the parabola \(y = 4x^2\)?

**Tip:** Remember, the sign of the coefficient \(a\) in the equation \(y = ax^2\) determines the direction the parabola opens.

Learn how to find the equation of a parabola that passes through the point (-1, 4) with its vertex at the origin (0, 0). This problem involves using the vertex form of a parabola and solving for the coefficient a. Suitable for high school students in Grades 10-12.

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