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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+
.??

1 answer

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.