Sketch the graph of this parabola y= -x² + 2

Answer 1

To sketch the graph of the parabola y = -x² + 2, we can start by determining a few key points and then connecting the dots.

1. y-intercept:
To find the y-intercept, substitute x = 0 into the equation. Thus, y = -0² + 2 = 2. Therefore, the parabola passes through the point (0, 2).

2. x-intercepts:
To find the x-intercepts, set y = 0 in the equation and solve for x.
0 = -x² + 2
x² = 2
x = ±√2
So, the parabola passes through the points (√2, 0) and (-√2, 0).

We can also plot a few other points to create a more accurate sketch:

3. x = -1:
Substituting x = -1, we get y = -(-1)² + 2 = -1 + 2 = 1. Thus, the point (-1, 1) is on the parabola.

4. x = 1:
Substituting x = 1, we get y = -(1)² + 2 = -1 + 2 = 1. Thus, the point (1, 1) is also on the parabola.

Now, plotting these points on a graph and connecting them:

Here is the sketch of the graph of the parabola y = -x² + 2: