How to show that a curve lies above the x-axis?

Expert replies

jspake: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Dec 09, 2012 6:06 am

by jspake » Sun Dec 09, 2012 6:36 am

Hello,
I couldn't figure out how to solve the question below:

The equation of a curve is y = x^2 âˆ’ 3x + 4.
Show that the whole of the curve lies above the x-axis.

Please help..

Like this post

Source: Beat The GMAT — Data Sufficiency | Sun Dec 09, 2012 6:36 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 09, 2012 9:11 am

jspake wrote:Hello,
I couldn't figure out how to solve the question below:

The equation of a curve is y = x^2 âˆ’ 3x + 4.
Show that the whole of the curve lies above the x-axis.

Please help..

Doesn't sound like a GMAT question to me.
What are the 5 answer choices?

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Sun Dec 09, 2012 12:35 pm

Remember the quadratic formula ?

E = ax^2 + bx + c = 0 iff x= (-b +- sqrt(b^2 - 4ac))/2a

if b^2 - 4ac < 0, E=0 has no real roots and E and a have the same sign for all real numbers x

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Dec 09, 2012 12:46 pm

jspake wrote:Hello,
I couldn't figure out how to solve the question below:

The equation of a curve is y = x^2 âˆ’ 3x + 4.
Show that the whole of the curve lies above the x-axis.

Please help..

Since we're helping you with your homework (Algebra II perhaps?), here's another approach.

Use the Complete the Square technique.
y = x^2 âˆ’ 3x + 4
y = x^2 âˆ’ 3x + 2.25 - 2.25 + 4 (completed the square)
y = (x - 1.5)^2 - 2.25 + 4 (factored)
y = (x - 1.5)^2 + 1.75 (simplified)

So, this parabola has its vertex at coordinates (1.5, 1.75), which means the vertex is above the x-axis.
Since the parabola opens up (which I'll leave you to convince your teacher of

), this parabola must lie above the x-axis.

Aside: For those studying for the GMAT (i.e., the vast majority of viewers), the Completing the Square technique is out of scope for the GMAT.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

savvysatyam: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sun Oct 28, 2012 8:09 pmFollowed by: 1 member; Thanked: 1 times

by savvysatyam » Mon Dec 10, 2012 2:03 am

Since a(the coefficient of quadratic equation) is greater than 0 and the determinant(b2)< 4ac, therfore it will be a parabola with face upwards and since determinant is not equal t zero it will be above x-axis and not touch it

Like this post

jspake: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun Dec 09, 2012 6:06 am

by jspake » Thu Dec 13, 2012 1:39 am

Thanks a lot guys..

Like this post

The Iceman: Master | Next Rank: 500 Posts; Posts: 194; Joined: Mon Oct 15, 2012 7:14 pmFollowed by: 6 members; Location: India; Thanked: 47 times

by The Iceman » Thu Dec 13, 2012 10:39 pm

Suppose we have a quadratic ax^2+bx+c=0

First, the sign of the coefficient of x^2 determines whether the parabola opens upwards or downwards. (a>0=> parabola opens up, and a<0=> parabola opens downwards)

Case 1: D=0 => Touches x axis at one point (significance: both roots real and equal)

Case 2: D>0 => Cuts x axis at two point (significance: the two roots are real and distinct)

Case 3: D<0 => Does not touch/cut/intercept x axis at any point (significance: both are non real roots)

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review