Question

Use the image to answer the question.

A parabola is graphed on a coordinate plane. The x-axis ranges from negative 1 to 10 in increments of 1. The y-axis ranges from negative 2 to 10 in increments of 1.

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

(2 points)
Standard form of the quadratic is y=
x2+
x+
.??

Answer 1

To write the equation of the quadratic function in standard form \( y = ax^2 + bx + c \), we need the vertex and a point the parabola passes through, or we can identify the coefficients from the graph based on its orientation and key points.

Without the image, I cannot provide the specific values for \( a \), \( b \), and \( c \), but I can guide you through the process of finding them:

1. **Identify the Vertex**: The vertex of the parabola is the highest or lowest point depending on the direction it opens.

2. **Pick Points on the Graph**: Choose at least one additional point that the parabola passes through if the vertex is not sufficient.

3. **Write the System of Equations**: Use the vertex and additional points to create a system of equations based on the standard form equation.

4. **Solve for a, b, and c**: Substitute the x and y coordinates of your chosen points into the standard form equation to find the coefficients.

If you are able to provide the coordinates of the vertex and a point on the parabola or describe the graph, I can help you write the specific equation.