Graphs of quadratic functions
Fill in a table for y = x2 − 2x − 3 with negative x and plot it, see why the bottom of a parabola is round, read the root (of an equation)s, y-intercept and turning point off the graph, and see what a does in y = ax2.
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Guide
To draw a parabola, fill in a table of values. Take care with negative x: (−2)² = 4, not −4, because a negative times a negative is positive.
Join the points with a smooth curve, not with a ruler. The bottom of a parabola is round, not pointed: between two points the curve dips a little below the straight line between them.
Where the parabola crosses the x-axis, y = 0, so those x-values are the root (of an equation)s of x2 − 2x − 3 = 0. Where it crosses the y-axis is the y-intercept. The turning point is the lowest (or highest) point, exactly halfway between the roots. In y = ax2, a negative a turns the parabola upside down, and the closer a is to 0, the wider it is.