Is (u,v) = (x square - x, x+1) a Parametric Form of a Parabola?

Click For Summary
SUMMARY

The parametric equations (u,v) = (x² - x, x + 1) represent a parabola. To verify this, one must express x in terms of v and substitute it back into the equation for u. This substitution confirms that u can be expressed solely in terms of v, thereby establishing the parametric form as a valid representation of a parabola.

PREREQUISITES
  • Understanding of parametric equations
  • Knowledge of quadratic functions
  • Familiarity with algebraic manipulation
  • Basic graphing skills
NEXT STEPS
  • Study the properties of parabolas in coordinate geometry
  • Learn about converting parametric equations to Cartesian form
  • Explore the implications of vertex form in quadratic equations
  • Investigate the graphical representation of parametric equations
USEFUL FOR

Students in mathematics, educators teaching algebra, and anyone interested in the geometric interpretation of parametric equations.

roberto dona
Messages
2
Reaction score
0
Hello. How can I verify that (u,v) = (x square - x, x+1) is a parametric form of a parabola? Thank you!
 
Physics news on Phys.org
Write x in terms of v and then replace it in the expression for u to obtain u in terms of v.
 
That works, thank you!
 

Similar threads

High School Geodesic dome parametric formula
  • · Replies 1 ·
Replies
1
Views
2K
MHB Evaluate the surface integral $\iint\limits_{\sum}f\cdot d\sigma$
  • · Replies 1 ·
Replies
1
Views
3K
MHB 12.5.4 Find parametric equations .
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Parameterize an offset ellipse and calculate the surface area
  • · Replies 5 ·
Replies
5
Views
3K
MHB How can we parametrize the triangle?
  • · Replies 16 ·
Replies
16
Views
19K
Undergrad Parametrization and kinematics
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Surface integrals/Surface areas of arbitrary domain regions
  • · Replies 3 ·
Replies
3
Views
2K
MHB Finding x of line bisecting parabola
  • · Replies 4 ·
Replies
4
Views
2K
MHB How Do You Calculate the Length of the Curve from $x=\ln{4}$ to $x=\ln{5}$?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Find ##\int_0^π \sin^ n x dx ##
  • · Replies 5 ·
Replies
5
Views
3K