find the intercepts and graph the equation by plotting points.
Y=2-2x^2
Y = 2 - 2x^2.
Y = -2x^2 + 2,
Let Y = 0 and calculate X:
-2x^2 + 2 = 0,
-2x^2 = -2,
x^2 = 1,
X = +-1. = X-intercepts.
Let X = 0 and calculate Y:
Y = -2*0^2 + 2 = 2 = Y-intercept.
h = Xv = -b / 2a = 0 / -4 = 0.
k = Yv = -2*0^2 + 2 = 2.
V(h,k) = V(0,2).
Use the following points for graphing:
(X,Y).
(-2,-6)
(-1,0)
V(0,2)
(1,0)
(2,-6).
To find the intercepts and graph the equation Y = 2 - 2x^2, we need to determine the x and y values where the equation intersects the x and y axes.
1. X-intercepts (where the graph intersects the x-axis):
To find the x-intercepts, we set Y = 0 and solve for x.
0 = 2 - 2x^2
Rearranging the equation, we get:
2x^2 = 2
x^2 = 1
x = ±√1
x = ±1
So, the x-intercepts are x = -1 and x = 1.
2. Y-intercept (where the graph intersects the y-axis):
To find the y-intercept, we set x = 0 and solve for Y.
Y = 2 - 2(0)^2
Y = 2 - 0
Y = 2
So, the y-intercept is Y = 2.
Now, let's plot these points on a graph:
- X-intercepts: (-1, 0) and (1, 0)
- Y-intercept: (0, 2)
Now, to graph the equation, we can plot a few more points to determine the shape of the graph. We'll choose some arbitrary x-values and calculate the corresponding y-values using the equation:
- For x = -2:
Y = 2 - 2(-2)^2
Y = 2 - 2(4)
Y = 2 - 8
Y = -6
- For x = -1:
Y = 2 - 2(-1)^2
Y = 2 - 2(1)
Y = 2 - 2
Y = 0
- For x = 0:
Y = 2 - 2(0)^2
Y = 2 - 2(0)
Y = 2 - 0
Y = 2
- For x = 1:
Y = 2 - 2(1)^2
Y = 2 - 2(1)
Y = 2 - 2
Y = 0
- For x = 2:
Y = 2 - 2(2)^2
Y = 2 - 2(4)
Y = 2 - 8
Y = -6
Now, we can connect these points on the graph. The graph of the equation Y = 2 - 2x^2 will be a downward-opening parabola passing through the points we plotted.
Here is a visual representation of the graph:
```
2 |
| x
| x x
| x x
| x x
| x x
_______|__x___x___x_______x_____|______
-2 -1 0 1 2
```
I hope this helps! Let me know if you have any further questions.