# Any Position of the Lines before Curves

|##### Definition

The position of the line have three possible position showed picture below.

For instance the line *g : y* = *mx + n* and parabolas *h : y = ax ^{2} + bx + c*.

When the equation of the line *g* is substituted over the parabola’s equation *h*, we get a new equation that is quadratic equation.

y* _{h}* = y

_{g}*ax ^{2} + bx + c* =

*mx + n*

*ax ^{2} + bx – mx+ c – n* =

*0*

*ax ^{2} + (b – m)x + (c – n)* =

*0*………….a new equation quadratic

The Discriminant (D) of the new equation is:

D = *(b – m)*^{2} – 4*a(c – n)*

By seeing the value of the discriminant’s equation quadratic, it show the position of the line *g* before parabolas *h* without to draw it graph first. This is main criteria :

- If D > 0, then the equation quadratic has two real values, so the line
*g*across parabolas*h*in two any point. - If D = 0, then the equation quadratic has two real same values, so the line
*g*offend the parabolas*h* - If D < 0, then the equation quadratic has no real values, so the line
*g*has no intersect nor offend to the parabolic*h*.

**Example 1**

*(Indonesian National Test)*

The graph of quadratic function is defined offend the line . The value b is fulfilled by…

*Alternative answer*

First step we have to make equal both of them. As we know that , thus we get equation

{quadratic equation}

The coefficient of quadratic equation is :

The condition is the equation quadratic has two real same values, so the line * *offend the parabolas

Discriminant = 0

So the values of b needed is b=3

**Example 2**

The line y = –2x + 3 offend a parabolas f(x) = x^{2} + (m – 1)x + 7, then the values m requirement is …

*Alternatif answer*

First step we have to make equals both of them. As we know that , thus we get equation

The coefficient of quadratic equation is :

The condition is the equation quadratic has two real same values, so the line * *offend the parabolas

Discriminant = 0

then we get a quadratic equation in variable m. By using factor’s solving we get

Hi, very nice website, cheers!

——————————————————

Need cheap and reliable hosting? Our shared plans start at $10 for an year and VPS plans for $6/Mo.

——————————————————

Check here: https://www.reliable-webhosting.com/

Esta é a empresa que uso para contratar meus seguros. https://renegade-angel.ch/mediawiki/index.php?title=Como_Funciona_Um_Protegido_Viagem

There’s certainly a great deal to know about this issue. I like all the points you’ve made.

trinidad and tobago dating http://statusuri.site/uk-dating/what-does-kik-mean-on-dating-sites.html 100 free dating sites nz

dating for cheaters review http://speeddate-com.onlinedatingfree.site/nudist-twister best dating site in south korea

buy erectile dysfunction pills online top erectile dysfunction pills buy erectile dysfunction pills online http://toperectiledysfunctionpills.com/

kink dating website http://mirrorhost.pw/uk-dating/dating-someone-with-a-toddler.html barbados dating service

augmented reality dating app http://uk-dating.top-online-dating.site/free-dating-sites-uk-no-credit-card free fuck dating sites

dating age rule http://plannibal.site/uk-dating/speed-dating-bristol-clifton.html iraq dating site

dating a single dad no time for me http://gratisdatingsites-nl.holten.site/top-3-dating-sites are katherine mcnamara and dominic sherwood dating

best irish dating websites http://infoshqip.site/dating/tagged-dating.html when did prince harry and meghan markle start dating

gay men dating women http://availan.site/dating/westlake-village-dating.html josh duhamel dating

gay mormon dating website http://celibatairesduweb-com.wjzx110.site/rencontres-vichy free dating sites in new hampshire

lovely bones essay http://sample-biology-lab-report-college.payforessay.design-group.site writing a law dissertation

essay on english subject http://dissertation-proposal-example-pdf_dissertation.buyessay.site online essay writer free

punk dating app http://bdsm-sex-dating.uk-dating.kpopersindonesia.site encounters dating discount

dating sites for green card http://dating-names-for-guys.uk-dating.nanoceramicshop.site free dating app and flirt chat match with singles

You are my aspiration, I own few blogs and sometimes run out from to brand : (.

Thanks for every other informative site. The place else could I am getting that kind of information written in such a perfect approach? I’ve a undertaking that I’m simply now working on, and I’ve been on the look out for such information.