https://file.aiquickdraw.com/mathbot/file/1726553849746dwmwfmbj.jpg

D.	What is the general form of the equation of the parabola below?

The graph you uploaded represents a parabola that appears to be oriented upwards, as the shape suggests, and passes through some specific points.

### Steps to find the general form of the equation:

The general form of a parabola is given by:

\[
y = ax^2 + bx + c
\]

To determine the exact form of the equation, we'll use the coordinates of the points that lie on the curve. Based on the graph, let's estimate the key points the parabola passes through:

1. \((2, 0)\)
2. \((4, 4)\)
3. \((6, 5)\)

We can use these points to form a system of equations to solve for \(a\), \(b\), and \(c\).

---

Let's calculate the coefficients now.The general equation of the parabola is:

\[
y = -\frac{3}{8}x^2 + \frac{17}{4}x - 7
\]

This equation is derived from the points on the graph and represents the parabola's curve.

Would you like further details on how this was calculated, or do you have any questions? Here are some related questions that could extend your understanding:

1. How can you convert this equation to vertex form?
2. How do you find the axis of symmetry for this parabola?
3. What is the significance of the coefficient \(a\) in the equation of a parabola?
4. How can you verify that the points lie on this parabola?
5. How does the discriminant of a quadratic equation relate to the shape of its graph?

**Tip**: When solving a system of equations, choosing points carefully from a graph helps ensure an accurate solution.

What is the general form of the equation of the parabola below?

This page explains how to find the general equation of a parabola using key points from the graph. It walks through calculating the coefficients in the quadratic equation form y = ax^2 + bx + c by solving a system of equations. Suitable for students in Grades 9-12.

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