The idea

Quadratic graphs

Why a quadratic draws a symmetric parabola, what the roots, y-intercept and turning point each are on the picture, and how the graph solves equations by intersection.

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Algebra · Graphs of functions

Quadratic graphs

Why a quadratic draws a symmetric parabola, what the roots, y-intercept and turning point each are on the picture, and how the graph solves equations by intersection.

Why it works

The mirror in the table

Plot

y = x^2 - 2x - 3

by feeding in

x

-values:

$x$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$y$	$5$	$0$	$-3$	$-4$	$-3$	$0$	$5$

The values fall then rise, and they MIRROR —

5, 0, -3, -4, -3, 0, 5

. That symmetry isn't luck: squaring treats

+

and

-

alike, so every parabola has a vertical line of symmetry through its lowest (or highest) point. The curve is smooth and U-shaped — never pointed, never made of line segments.

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The rest of the explanation, plus 2 worked examples you step through move by move.

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