Let's learn about the graph of $y = x^2$ step by step! 🎉
1. Imagine you have some numbers for $x$: -2, -1, 0, 1, 2.
2. For each $x$, we find $y$ by multiplying $x$ by itself: $y = x \times x$.
3. Let's see the pairs:
**Box 1:**
Group 1: x values
-2️⃣ -1️⃣ 0️⃣ 1️⃣ 2️⃣
(5 numbers)
Add ➕
**Box 2:**
-2️⃣ -1️⃣ 0️⃣ 1️⃣ 2️⃣
(5 numbers)
Group 2: y values ($x^2$)
4️⃣ 1️⃣ 0️⃣ 1️⃣ 4️⃣
(5 numbers)
=
**Total box:**
4️⃣ 1️⃣ 0️⃣ 1️⃣ 4️⃣
(5 numbers)
Pairs (x, y)
(-2,4) (-1,1) (0,0) (1,1) (2,4)
4. Now, if we put these points on a graph, we get a U shape called a parabola! 🌈
5. The lowest point is at $(0,0)$, called the vertex.
6. The graph is symmetric, it looks the same on both sides.
Great job! You just learned how to make a graph from the equation $y = x^2$. 🎯(-2,4) (-1,1) (0,0) (1,1) (2,4)