https://file.aiquickdraw.com/mathbot/file/17211768199429rl6g368.png

The graph shown in the image is of a quadratic function (a parabola) that opens upwards. From the graph, we can observe the following key features:

1. The vertex of the parabola is at the point (0, 1), indicating the minimum value of the function.
2. The axis of symmetry is the vertical line \(x = 0\), which suggests the quadratic function has no horizontal shift.
3. The parabola intersects the y-axis at \(y = 1\), which means the y-intercept of the function is 1.

A general form of a quadratic function is \( f(x) = ax^2 + bx + c \). Given the above observations:
- Since the vertex is at (0, 1), the function can be written as \( f(x) = ax^2 + 1 \).
- The coefficient \( a \) determines the width and direction of the parabola. To find \( a \), we need another point on the graph.

From the graph, we can see the points (-1, 2) and (1, 2). Plugging these into the function, we get:
\[ 2 = a(1)^2 + 1 \]
\[ 2 = a + 1 \]
\[ a = 1 \]

So the function is:
\[ f(x) = x^2 + 1 \]

If you have any questions or want more details, feel free to ask! Here are five more questions you might consider:

1. How do you determine the vertex of a quadratic function?
2. What is the axis of symmetry in a quadratic function and how do you find it?
3. How can you find the y-intercept of a quadratic function?
4. How do you determine the coefficient \( a \) in a quadratic function?
5. How do the coefficients \( a \), \( b \), and \( c \) affect the shape and position of a parabola?

**Tip:** To find the exact form of a quadratic function from its graph, identify the vertex and another point on the parabola to solve for the coefficients.

Explore how to determine the function of a quadratic graph with a detailed explanation. Learn about the vertex, axis of symmetry, y-intercept, and coefficient in quadratic functions. Suitable for high school students.

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