https://file.aiquickdraw.com/mathbot/file/17266121414388qrgvrda.jpg

From the image, it's clear that the vertex of the parabola is at \( (0, -5) \) and it opens upwards. This vertex point can be used to write the vertex form of the equation of the parabola.

### Vertex Form
The general vertex form of a parabola is:
\[ y = a(x - h)^2 + k \]
where \( (h, k) \) is the vertex of the parabola. Here, \( h = 0 \) and \( k = -5 \), so the equation simplifies to:
\[ y = a(x - 0)^2 - 5 \]
or
\[ y = ax^2 - 5 \]

### Finding the Coefficient \( a \)
To find the coefficient \( a \), we can use another point on the parabola. The parabola also passes through the point \( (3, -2) \). Substituting \( x = 3 \) and \( y = -2 \

Write an equation of the parabola in vertex form or intercept form. The vertex is at (0, -5), and the parabola passes through the point (3, -2).

Learn how to write the equation of a parabola in vertex form, given its vertex at (0, -5) and passing through the point (3, -2). Includes detailed step-by-step solutions using vertex form and solving for the 'a' value.

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