SOLUTION: sketch a graph of all the (x,y)coordinates that satisfy the equation y-x2=-1. What shape is the graph?

Algebra ->  Linear-equations -> SOLUTION: sketch a graph of all the (x,y)coordinates that satisfy the equation y-x2=-1. What shape is the graph?      Log On


   

Question 174319This question is from textbook algebra 1
: sketch a graph of all the (x,y)coordinates that satisfy the equation
y-x2=-1. What shape is the graph? This question is from textbook algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y-x%5E2=-1 Start with the given equation.


y=x%5E2-1 Add x%5E2 to both sides.




Table of Contents:


Jump to Table
Jump to Graph


In order to graph y=x%5E2-1, we need to plot some points.


Let's find y when x=-3
(Note: you can start with any x-value):


y=x%5E2-1 Start with the given equation.


y=%28-3%29%5E2-1 Plug in x=-3.


y=9-1 Square -3 to get 9.


y=8 Combine like terms.


So when x=-3, then y=8.


So we have the point .


----------------------------------------------------


Let's find y when x=-2:


y=x%5E2-1 Start with the given equation.


y=%28-2%29%5E2-1 Plug in x=-2.


y=4-1 Square -2 to get 4.


y=3 Combine like terms.


So when x=-2, then y=3.


So we have the point .


----------------------------------------------------


Let's find y when x=-1:


y=x%5E2-1 Start with the given equation.


y=%28-1%29%5E2-1 Plug in x=-1.


y=1-1 Square -1 to get 1.


y=0 Combine like terms.


So when x=-1, then y=0.


So we have the point .


----------------------------------------------------


Let's find y when x=0:


y=x%5E2-1 Start with the given equation.


y=%280%29%5E2-1 Plug in x=0.


y=0-1 Square 0 to get 0.


y=-1 Combine like terms.


So when x=0, then y=-1.


So we have the point .


----------------------------------------------------


Let's find y when x=1:


y=x%5E2-1 Start with the given equation.


y=%281%29%5E2-1 Plug in x=1.


y=1-1 Square 1 to get 1.


y=0 Combine like terms.


So when x=1, then y=0.


So we have the point .


----------------------------------------------------


Let's find y when x=2:


y=x%5E2-1 Start with the given equation.


y=%282%29%5E2-1 Plug in x=2.


y=4-1 Square 2 to get 4.


y=3 Combine like terms.


So when x=2, then y=3.


So we have the point .


----------------------------------------------------


Let's find y when x=3:


y=x%5E2-1 Start with the given equation.


y=%283%29%5E2-1 Plug in x=3.


y=9-1 Square 3 to get 9.


y=8 Combine like terms.


So when x=3, then y=8.


So we have the point .


----------------------------------------------------





Jump to Top of Page
Now let's make a table of the values we just found.


Table of Values:





xy
-38


-23


-10


0-1


10


23


38

Now let's plot the points:







Jump to Top of Page

Graph:


Now draw a curve through all of the points to graph y=x%5E2-1:


Graph of y=x%5E2-1 (which is also the graph of y-x%5E2=-1)


So the shape of y-x%5E2=-1 is a parabola.