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 determine the equation of the quadratic function in standard form \( y = ax^2 + bx + c \), we need to identify three key points on the parabola: the vertex and two additional points, or the y-intercept and any other point.

**1. Identify the Vertex:**
- If you can see the vertex on the graph, note its coordinates. Let's say the vertex is at \( (h, k) \).

**2. Identify another point:**
- Look for another distinct point on the parabola. For example, if the parabola passes through \( (x_1, y_1) \).

**3. Write the standard form equation:**
- Use the vertex form of a quadratic equation, which is \( y = a(x - h)^2 + k \).
- Plug in the vertex coordinates and the coordinates of the other point to solve for \( a \).

**4. Convert to standard form:**
- Expand the vertex form to obtain the standard form \( y = ax^2 + bx + c \).

Since I don't have access to the image itself or specific points, I can't compute exact values. If you provide the coordinates of the vertex and another point, I can walk you through to find the equation.