Y equals 'a' times x squared, plus b times x, plus c.

Here, b and c are both 0, so the equation reduces to: Y = 'a' times x squared.

(Any number squared is that number times itself, so if x is 7, x squared becomes 49.)

What we're looking at above, is a set of some 33 parabolas, depending on the value of 'a'.

In reading this graph, x is horizontal, and Y is vertical.

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Beginning with the sharpest of the lower curves, 'a' equals -4.

By the magenta trace, 'a' has increased to -1.

The horizontal line at center represents an 'a' value of 0; 0 times x squared equals 0, always.

(Zero is a strange figure, but more on that elsewhere.)

By the time of the blue trace, 'a' is now positive 1.

And so this trend continues to the tightest of the upper traces, where 'a' equals 4.

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The lessons here?

Parabolas where 'a' is positive run high-low-high, they point downward.

Parabolas where 'a' is negative run low-high-low, they point upward.

The greater the absolute value of 'a', the sharper the parabola will be.

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The "absolute value"? .This is how far a number is away from 0.

The absolute value of 4 is 4, it's 4 away from 0.

The absolute value of -6 is 6, because it's 6 away from 0, just in the other direction.

Another way of putting it is, "absolute value" is about the number, not the sign.

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The direction the curve faces, is about the sign.

The intensity of the curve, is about the absolute value of 'a'.