The image displays a quadratic function graph and a multiple-choice question asking which of the following functions best describes the given graph. Let's analyze it:

The key observations about the graph are:

1. It is a parabola that opens upwards, which indicates a positive $x^2$-term.
2. The vertex appears to be around $x = 4$ and the parabola passes through the y-axis above the x-axis (around $y = 16$).

We are given four options:

• A. $y = x^2 - 8x + 18$
• B. $y = x^2 + 9x + 20$
• C. $y = x^2 + x - 12$
• D. $y = x^2 - 9x + 20$

Let's test these options by considering their general behavior:

• Option A, $y = x^2 - 8x + 18$, has a minimum, but its vertex and y-intercept don't match the graph's characteristics.
• Option B, $y = x^2 + 9x + 20$, opens upwards, but again its vertex and y-intercept seem off.
• Option C, $y = x^2 + x - 12$, has a vertex and general shape that do not match.
• Option D, $y = x^2 - 9x + 20$, opens upwards and has a y-intercept of 20, which fits the graph's appearance.

Thus, Option D seems to be the best match for this quadratic graph based on its intercepts and the shape of the curve.

Would you like a detailed explanation of how to verify this algebraically or any other help?

Here are five related questions for you:

1. How do you find the vertex of a quadratic function?
2. What role does the coefficient of the $x^2$-term play in a parabola's shape?
3. How can you determine the y-intercept of a quadratic function?
4. What is the significance of the discriminant in a quadratic function?
5. How do you complete the square to transform a quadratic function?

Tip: To quickly identify a quadratic function's graph, focus on its vertex and y-intercept, which are easy to spot and match with the equation.