describe change from y = x^2 to y = x^2 - 1
- Thread starter shawnka
- Start date
Do this:
1. Get out your calculator (I'm assuming that since you're in an advanced math course, you have a graphing calc.)
2. Hit the Y= button
3. In the \Y1= spot, type \Y1=x^2
4. Hit the GRAPH button on your calculator and look at the parabola that appears from the y=x^2 formula.
5. Now hit the Y= button again and go to the space with \Y2
6. In \Y2= type this: \Y2=(x^2)-1 the parentheses are used to reduce confusion on this forum. I would suggest using them in the equation as well though, since it's a good habit.
7. Press GRAPH and note that the new parabola moves 1 point down when the -1 is tacked onto the end of the equation. That is the difference created from changing the equation of... y=x^2 into y=(x^2)-1
The -1 essentially says "ok, lets move the point where the parabola branches (the curvy line things that look like a bowl) touch the Y-axis down one, meeting at the point (0,-1). Thus if the equation were--->
y=(x^2)-2 the parabola branches would meet at the point (0,-2) Or, if the equation was---> y=(x^2)+5 the parabola would move up 5 spots on the Y-axis {moving from the point (0,0)} to the point of (0,5)
Hope this helps
1. Get out your calculator (I'm assuming that since you're in an advanced math course, you have a graphing calc.)
2. Hit the Y= button
3. In the \Y1= spot, type \Y1=x^2
4. Hit the GRAPH button on your calculator and look at the parabola that appears from the y=x^2 formula.
5. Now hit the Y= button again and go to the space with \Y2
6. In \Y2= type this: \Y2=(x^2)-1 the parentheses are used to reduce confusion on this forum. I would suggest using them in the equation as well though, since it's a good habit.
7. Press GRAPH and note that the new parabola moves 1 point down when the -1 is tacked onto the end of the equation. That is the difference created from changing the equation of... y=x^2 into y=(x^2)-1
The -1 essentially says "ok, lets move the point where the parabola branches (the curvy line things that look like a bowl) touch the Y-axis down one, meeting at the point (0,-1). Thus if the equation were--->
y=(x^2)-2 the parabola branches would meet at the point (0,-2) Or, if the equation was---> y=(x^2)+5 the parabola would move up 5 spots on the Y-axis {moving from the point (0,0)} to the point of (0,5)
Hope this helps