The question asks to "Express the quadratic function in standard form" for the function:

$f(x) = 2x^2 + 8x + 9$

This function is already in the standard form for a quadratic equation, which is generally expressed as:

$f(x) = ax^2 + bx + c$

Where:

• $a = 2$ (coefficient of $x^2$),
• $b = 8$ (coefficient of $x$),
• $c = 9$ (constant term).

Thus, the quadratic function provided, $f(x) = 2x^2 + 8x + 9$, is already in its standard form.

Would you like to explore how to find the vertex form of this equation or further explanations?

Here are some related questions:

1. How do you convert a quadratic function to vertex form?
2. What is the significance of the coefficients $a$, $b$, and $c$ in the quadratic function?
3. How do you find the vertex of a quadratic function using the standard form?
4. What is the general shape of the graph of the quadratic function $f(x) = ax^2 + bx + c$?
5. How do you determine the direction in which the parabola opens?

Tip: For any quadratic function, the sign of $a$ determines whether the parabola opens upwards or downwards.