Solution to find the value of (x) in the (y = 2 - x²)?

Question

I have to turn (y = 2 - x²) into a graph but I've been stuck on this for a very long time, and while I know what the answer is and what the graph should look like I have no idea how to get to the answer.

Could anyone please be really kind and explain the steps to solving for (x) so I can understand? I'd be extremely grateful.

Answer 1

Given functiion y = 2-x^2

Subtract 2 from each side.

y-2 = 2-2-x^2

-x^2 = y-2

Multiple to each side by negitive one.

x^2 = 2-y

Apply squre root on each side.

x = √(2-y)

For y = 0 then x = √2 = ±1.414

For y = 1 then x = √1 = ± 1

For y = 2 then x = 0

For y = -1 then x = √3 = ±1.732

For y = -2 then x = √4 = ±2

Graph of y = 2-x^2

From the graph we can observe the each solution of x for above y values.

Solution: the value of x = √(2-y).

Comments

Choose values for y and find the corresponding values for x.

y	x = √(2 - y)	(x, y)
- 2	x = √4 = ± 2	(± 2, - 2)
- 1	x = √3 = ± 1.732	(± 1.732, - 1)
0	x = √2 = ± 1.414	(± 1.414, 0)
1	x = √1 = ± 1	(± 1, 1)
2	x = 0	(0, 2)

1.Draw a coordinate plane.

2.Plot the coordinate points.

3.Then sketch the graph, connecting the points with a smooth curve.