From the image, we have two types of questions:

1. Graphs (33 and 34): These display parabolas, and you're likely being asked to describe characteristics of the parabola, such as vertex, axis of symmetry, and domain/range.

2. Exercises 35-42: The goal is to rewrite each function in the form $f(x) = a(x - h)^2 + k$, which is the vertex form of a parabola. This involves completing the square and identifying the vertex.

I'll walk through one example of completing the square for these exercises.

Example: Exercise 35

We are given:
$f(x) = x^2 - 3x$

To convert this to vertex form, we complete the square:

1. Factor out the coefficient of $x^2$, but here it's 1, so we skip this step.
2. Take half the coefficient of $x$ (which is -3), square it, and add and subtract it inside the equation: $x^2 - 3x = \left( x^2 - 3x + \left( \frac{-3}{2} \right)^2 \right) - \left( \frac{-3}{2} \right)^2$ $= (x - \frac{3}{2})^2 - \frac{9}{4}$

Thus, the vertex form is: $f(x) = (x - \frac{3}{2})^2 - \frac{9}{4}$

The vertex is $\left( \frac{3}{2}, -\frac{9}{4} \right)$.

Would you like me to solve the rest or provide more details on completing the square?

Relative Questions:

1. What is the process for finding the axis of symmetry for a parabola?
2. How do you determine if a parabola opens upwards or downwards?
3. What is the relationship between the vertex form of a quadratic and its graph?
4. How do you calculate the y-intercept of a quadratic function?
5. What are the key differences between the standard form and vertex form of a quadratic function?

Tip: In vertex form $f(x) = a(x - h)^2 + k$, the vertex is $(h, k)$, and the value of $a$ tells you whether the parabola opens up or down (positive opens upwards, negative opens downwards).