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pmiz07 pmiz07
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12 years ago
I have a math project and was just wondering what effect the "b value" of a quadratic in standard form has on the shape of the parabola, if any. Thanks.
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#1
12 years ago
it represents the coefficient of x
Eg   4x^2 + 5x + 6

4 is the coefficient of x^2
5 is the coefficient of x
6 is the constant
wrote...
#2
12 years ago
The simplest way to explain how the b value affects the shape of the graph of a parabola is to say that it adjusts where on the actual parabola crosses a given point.

Say, x^2+0x+0  .... that is a parabola that is centered on the origin.

If you change the b value to say, 10
x^2 +10x+0   ... now the lowest point of the parabola is not on the origin.  The parabola still passes right through the origin, but relatively, the origin has moved up one leg of the parabola, and the shape is exactly the same.  Another way to say it is that the parabola is the same shape and still passes through the origin, but the low point of the parabola has been moved down and to the left.

The best idea is to plug some examples into a graphing calculator and only change the b value... then compare the results.  You'll see that the parabola is the same size and shape and width, and that they all intersect at one point.  But relative to each parabola, that point is in a different spot on the actual parabola, depending on the value of b.
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