A parabola is set of all points in a aircraft which room an equal distance away native a given point and offered line. The point is dubbed the focus that the parabola and also the heat is called the directrix.

The emphasis lies ~ above the axis of the contrary of the parabola.

You are watching: Which equation describes a parabola that opens up or down and whose vertex is at the point (h, v)?


Finding the emphasis of a parabola provided its equation

If you have actually the equation the a parabola in vertex form y=a(x−h)2+k, climate the vertex is at (h,k) and the focus is (h,k+14a).

Notice that right here we space working v a parabola with a vertical axis of symmetry, so the x-coordinate of the focus is the exact same as the x-coordinate of the vertex.

Example 1:

find the focus of the parabola y=18x2.

Here h=0and k=0, therefore the crest is in ~ the origin. The works with of the emphasis are (h,k+14a) or (0,0+14a).

Since a=18, us have



The emphasis is at (0,2).


Example 2:

uncover the emphasis of the parabola y=−(x−3)2−2.

Here h=3 and k=−2, therefore the peak is in ~ (3,−2). The coordinates of the emphasis are (h,k+14a) or (3,−2+14a).

Here a=−1, therefore



The focus is at (3,−2.25).


Subjects near Me
polite Procedure Tutors ACT courses & classes IB background Tutors Montana Bar Exam courses & class MLT exam Tutors Planetary Geology Tutors CompTIA A+ check Prep super Smash Bros. Melee Tutors six Sigma training ParaPro test Tutors collection 32 courses & great Certified clinical Assistant test Test prep SSAT test Prep 2nd Grade English Tutors Islamic studies Tutors SAT topic Test in biological E/M process & classes GRE subject Test in Chemistry check Prep Illinois Bar Exam courses & classes Google cultivate GCSE architecture and an innovation Tutors
Popular Cities
Nashville Tutoring Phoenix Tutoring mountain Francisco-Bay Area Tutoring Orlando Tutoring Indianapolis Tutoring las Vegas Tutoring Albany Tutoring Chicago Tutoring Tucson Tutoring Seattle Tutoring
Popular Subjects
ISEE Tutors in san Diego GRE Tutors in Atlanta reading Tutors in Dallas ft Worth LSAT Tutors in Seattle biological Tutors in Boston MCAT Tutors in Chicago Statistics Tutors in Dallas fort Worth SSAT Tutors in Seattle Calculus Tutors in Philadelphia SSAT Tutors in Miami

Download our cost-free learning devices apps and test prep books

Show More

Varsity Tutors
Our Company
Free Resources
Top Subjects
Top Locations
Show legit DisclaimerHide legitimate DisclaimerPrivacy PolicyTerms the UseSitemapSign In

Names of standardization tests are owned by the trademark holders and also are no affiliated through Varsity Tutors LLC.

*See finish details for better Score Guarantee.

Media outlet trademarks space owned by the particular media outlets and also are not affiliated through Varsity Tutors.

Award-Winning claim based on CBS Local and Houston push awards.

Varsity Tutors does not have affiliation v universities pointed out on the website.

See more: How Do You Say Welcome To Mexico In Spanish ? How Do You Say Welcome To Mexico In Spanish

Varsity Tutors connect learners through experts. Instructors are independent contractors who tailor their solutions to every client, utilizing their own style,methods and also materials.