https://file.aiquickdraw.com/mathbot/file/1728508294735y5uj3ygn.jpg

The graph shows a parabola that opens upwards. To determine its equation, we need to identify the standard form of a quadratic function:

\[
f(x) = ax^2 + bx + c
\]

### Key Observations
1. **Vertex**: The lowest point of the parabola is at \( (4, 0) \). This tells us that the vertex is at \( x = 4 \), and \( f(4) = 0 \).
2. **Symmetry and Axis**: The parabola is symmetric around \( x = 4 \). This suggests it can be expressed as \( f(x) = a(x - 4)^2 \).
3. **Point Analysis**: From the graph, the parabola passes through \( (2, 4) \) and \( (6, 4) \). Plugging in \( (2, 4) \) into \( f(x) = a(x - 4)^2 \):

\[
4 = a(2 - 4)^2 = a(-2)^2 = 4a \implies a = 1
\]

### Final Equation
The equation in expanded form is:

\[
f(x) = (x - 4)^2 = x^2 - 8x + 16
\]

Thus, the standard form of the equation is:

\[
f(x) = x^2 - 8x + 16
\]

You can fill in the values as follows:

\[
\boxed{1} x^2 \, + \, \boxed{-8} x \, + \, \boxed{16}
\]

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### Related Questions
1. How do you find the vertex of a parabola given its equation?
2. What does the value of \( a \) tell us about the direction of a parabola?
3. How do we use symmetry to determine additional points on a parabola?
4. What are the different forms of a quadratic equation?
5. How can you determine the y-intercept of a parabola?

**Tip**: When the parabola is given graphically, identifying the vertex and one other point can help determine the entire equation.

Determine the equation of the parabola graphed below.

Learn how to find the equation of a parabola with a vertex at (4, 0) and additional points on the graph. This problem explores key concepts in quadratic functions and algebra, perfect for students in grades 9-11.

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