# quadratics graphs

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• Sep 15th 2009, 07:08 AM
mark
quadratics graphs
hi,

i'm doing a question on cubic graphs and i was told that if there is a squared value involved the graph line will touch rather than cross directly the x axis. i've come to a question that is \$\displaystyle y = (x - 2)(x^2 + 2x + 4)\$ so i thought it may touch because it has a square value then realised it doesn't when i looked at the answer. so i thought maybe i should factorise the quadratic equation but i don't think you can? what has gone wrong here?

thanks, mark

ah i've just realised the quadratic formula might need to be used, any input would still be appreciated though
• Sep 15th 2009, 07:16 AM
mathaddict
Quote:

Originally Posted by mark
hi,

i'm doing a question on cubic graphs and i was told that if there is a squared value involved the graph line will touch rather than cross directly the x axis. i've come to a question that is \$\displaystyle y = (x - 2)(x^2 + 2x + 4)\$ so i thought it may touch because it has a square value then realised it doesn't when i looked at the answer. so i thought maybe i should factorise the quadratic equation but i don't think you can? what has gone wrong here?

thanks, mark

ah i've just realised the quadratic formula might need to be used, any input would still be appreciated though

That's only when the whole factor is squared .. ie \$\displaystyle (x-a)^2\$ ,

\$\displaystyle x^2 + 2x + 4\$ is complex ..
• Sep 15th 2009, 07:20 AM
mark
what about just the discriminant part of the quadratic formula?