To draw the graph of the function y = x², start by plotting a few key points. The function is a parabola that opens upwards. You can calculate the value of y for different values of x:
- If x = -2, then y = (-2)² = 4
- If x = -1, then y = (-1)² = 1
- If x = 0, then y = 0² = 0
- If x = 1, then y = 1² = 1
- If x = 2, then y = 2² = 4
Plot these points on a graph. You should see that as x values increase or decrease, the y values also increase, forming a U-shaped curve.
Next, let’s solve the equation x² – 1 = 0. To do this, we can rearrange the equation:
x² = 1
Now, take the square root of both sides:
x = ±1
Thus, the solutions to the equation x² – 1 = 0 are x = 1 and x = -1.
In summary, the graph of y = x² is a parabola, and the equation x² – 1 = 0 has two solutions: 1 and -1.