Let's break down each transformation and plot them on the provided graph.

Original Function: $f(x) = x^2$

This is the standard parabola opening upwards with its vertex at the origin $(0, 0)$.

Move 1: Jump Up

• Transformation: Vertical shift up by 3 units.
• Equation: $f(x) = x^2 + 3$
  • The entire parabola moves 3 units up, so the new vertex is at $(0, 3)$.

Move 2: Slide Left

• Transformation: Horizontal shift left by 2 units.
• Equation: $f(x) = (x + 2)^2$
  • The parabola shifts 2 units to the left, so the new vertex is at $(-2, 0)$.

Move 3: Flip

• Transformation: Reflection over the x-axis.
• Equation: $f(x) = -x^2$
  • The parabola is reflected over the x-axis, so it opens downwards with the vertex at the origin $(0, 0)$.

I'll now outline the steps you would take to manually plot these on the graph.

1. Plot the original function $f(x) = x^2$:

   • Start at the origin $(0,0)$ and plot the parabola opening upwards.

2. Plot $f(x) = x^2 + 3$:

   • Shift every point on the original parabola 3 units up.

3. Plot $f(x) = (x + 2)^2$:

   • Shift every point on the original parabola 2 units to the left.

4. Plot $f(x) = -x^2$:

   • Reflect the original parabola over the x-axis.

Since I can't directly plot these on the graph for you, I can guide you through the process. However, if you want to visualize these steps on your graph, you can manually sketch each transformed function.

Would you like more details or have any