The image contains the following problem based on transformations of the function $f(x) = x^2$:

Problem: Starting with the graph of $f(x) = x^2$, write the equation of the graph that results from:

(a) Writing $f(x)$ 3 units upwards:
$y = \_\_\_\_\_$

(b) Shifting $f(x)$ 2 units to the left:
$y = \_\_\_\_\_$

(c) Reflecting $f(x)$ about the x-axis:
$y = \_\_\_\_\_$

Solutions:

1. (a) Writing $f(x)$ 3 units upwards:
   To shift a function $f(x)$ upwards by $k$ units, you add $k$ to the function:
   $y = f(x) + 3 = x^2 + 3$

2. (b) Shifting $f(x)$ 2 units to the left:
   To shift a function $f(x)$ left by $h$ units, you replace $x$ with $x + h$:
   $y = f(x + 2) = (x + 2)^2$

3. (c) Reflecting $f(x)$ about the x-axis:
   To reflect a function $f(x)$ about the x-axis, you multiply the function by $-1$:
   $y = -f(x) = -x^2$

Would you like further details on transformations or have any questions about these steps? Here are 5 related questions:

1. How would you shift $f(x)$ by 4 units to the right?
2. What would the equation be if $f(x)$ was reflected over the y-axis instead of the x-axis?
3. How do you vertically stretch $f(x) = x^2$ by a factor of 2?
4. How can we reflect $f(x)$ over both the x-axis and the y-axis?
5. What happens to the graph when you shift it both horizontally and vertically?

Tip: When shifting graphs, always check whether the shift is horizontal or vertical, as each type has a different effect on the equation.