quadratic equations

**mark** · August 27th 2009, 09:43 AM

hi, i've got a few questions from my book where i'm sure the answers in the back are wrong. the quadratic is factorised into $(x - 2) (x - 1)$ the parabolas cross the x axis at 2 and 1 it then asks me what shape the graph would be. i would think that it would be an inverted U shape (ie like an "n" shape) but the book says its U shaped. similarly with $(x + 3) (x + 4)$ i would expect the opposite of a U shape but the book says it actually is U shaped. am i wrong?

**masters** · August 27th 2009, 10:13 AM

Originally Posted by mark

hi, i've got a few questions from my book where i'm sure the answers in the back are wrong. the quadratic is factorised into $(x - 2) (x - 1)$ the parabolas cross the x axis at 2 and 1 it then asks me what shape the graph would be. i would think that it would be an inverted U shape (ie like an "n" shape) but the book says its U shaped. similarly with $(x + 3) (x + 4)$ i would expect the opposite of a U shape but the book says it actually is U shaped. am i wrong?

Hi mark,

Using the standard quadratic form:

$y=ax^2+bx+c$

If a > 0, then the parabola opens up.

If a < 0, then the parabola opens down.

Your example: $y=(x-2)(x-1)$ would be $y=x^2-3x+2$ .

Since a = 1, the graph is a parabola that opens upward. The same thing happens with your other example: $y=(x+3)(x+4)$ . This becomes $y=x^2+7x+12$ and since a = 1, opens upward as well.

**apcalculus** · August 27th 2009, 10:13 AM

Originally Posted by mark

hi, i've got a few questions from my book where i'm sure the answers in the back are wrong. the quadratic is factorised into $(x - 2) (x - 1)$ the parabolas cross the x axis at 2 and 1 it then asks me what shape the graph would be. i would think that it would be an inverted U shape (ie like an "n" shape) but the book says its U shaped. similarly with $(x + 3) (x + 4)$ i would expect the opposite of a U shape but the book says it actually is U shaped. am i wrong?

If the coefficient of the x^2 term is positive, then you have a U shaped parabola (opening upward). If the coefficient of x^2 is negative, you have an inverted U shape. In both your examples the coefficient of x^2 is positive -- try expanding the product in your head.

Good luck!

**nikhil** · August 27th 2009, 10:18 AM

(x-2)(x-1)
so you know that it will be a parabola so it will be some sort of U now
at x=infinity you will get a positive value and also for x=-infinity you will get a positive value so the graph is such a u that is only above x axis and such a u is U not n.
similarly you can try for other equation.
otherwise you may trace the graph using calculus

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