Graphing Parabola, negative x values

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
wp_913
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Graphing Parabola, negative x values

Postby wp_913 » Sun May 13, 2012 2:23 pm

Hi

I'm confused, a negative number with an exponent (exponentiation), will first have the exponent evaluated, and then have the opposite applied, ie. -2^2 = -4

However, if the negative number is enclosed with parentheses, (-2)^2, that indicates (-2) x (-2) = 4

So my question, when finding points for graphing a parabola, it appears from the examples I have studied that any negative values for x^2 always come out positive when evaluated in the quadratic equation, but there are no parentheses enclosing that value.

f(x) = ax^2 + bx + c

f(-2) = -2^2 + 4(-2) + 3 = -9, but all the examples that I study would evaluate this as f(-2) = (-2)^2 + 4(-2) + 3 = -1. But the parentheses are not shown, what rule or concept am I missing?

Thanks in advance.

theshadow
Posts: 105
Joined: Sun Feb 22, 2009 11:12 pm

Re: Graphing Parabola, negative x values

Postby theshadow » Sun May 13, 2012 3:53 pm

Without seeing your book, it's hard to say what's going on. Does the book show the plug-and-chug as "-2^2 = 4", etc?

wp_913
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Joined: Mon May 16, 2011 12:01 am
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Re: Graphing Parabola, negative x values

Postby wp_913 » Sun May 13, 2012 4:37 pm

Hi

Not sure what the plug - chug means

This is what the book shows:

A negative number with an exponent (exponentiation), will first have the exponent evaluated, and then have the opposite applied, ie. -2^2 = -4

However, if the negative number is enclosed with parentheses, (-2)^2, that indicates (-2) x (-2) = 4

But in later chapters evaluating and graphing quadratic equations:

when finding points for graphing a parabola, it appears from the examples I have studied that any negative values for x^2 always come out positive when evaluated in the quadratic equation, but there are no parentheses enclosing that value.

f(x) = ax^2 + bx + c

f(-2) = -2^2 + 4(-2) + 3 = -9, but all the examples that I study would evaluate this as f(-2) = (-2)^2 + 4(-2) + 3 = -1. But the parentheses are not shown, what rule or concept am I missing?

Let me know if I can explain this better?

theshadow
Posts: 105
Joined: Sun Feb 22, 2009 11:12 pm

Re: Graphing Parabola, negative x values

Postby theshadow » Mon May 14, 2012 1:38 am

They don't put the parens around the variable x because you know what that is: the variable x. They do put the parens around the numbers, because otherwise it might be confusing. If you have x^2 and plug something in that's negative, if you don't use parens then it's confusing: x^2 for x = -1 should be "the square of -1". If you do "-1^2", then it looks like you mean "the negative of the square of 1" which isn't what you mean. If you do "(-1)^2", then you're saying what you mean.

So I think it's using punctuation to make the meaning clear, but not using that punctuation when you don't actually need it, like when it's variable instead of numbers.


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