Use the image to answer the question.

Question

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 6 to 6 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 1.

Write the equation of the quadratic function in the graph in standard form.

(2 points)
The standard form of the quadratic is y=
x2+
x+
.
Remaining Attempts : 3

Answer 1

To determine the equation of the parabola in standard form \(y = ax^2 + bx + c\), we typically need to identify specific points on the graph, particularly the vertex and at least one additional point.

Since I don't have access to the image, you should look for these key pieces of information from the graph:

1. Vertex: This is the highest or lowest point of the parabola. The coordinates of the vertex will be critical to formulating the equation.

2. Direction: Determine if the parabola opens upward or downward. If it opens upward, \(a > 0\); if it opens downward, \(a < 0\).

3. Intercepts: Identify y-intercept (when \(x = 0\)) and x-intercepts (when \(y = 0\)), if visible. These can help in solving for \(b\) and \(c\) or confirming your equation.

Once you gather this information, you can substitute into the standard form equation.

For example, if you find that the vertex is at \( (h, k) \) and you know the value of \( a \), you might use vertex form \(y = a(x - h)^2 + k\) and expand to standard form.

After determining approximate values for \(a\), \(b\), and \(c\), you would construct the standard form equation.

If you need more help, provide specific coordinates or features of the parabola from the graph!