To draw the graph of a quadratic function accurately, work out a table of values, choose a scale for each axis, plot the points and join them with a smooth curve. **Table for y=x2-x-2** x | -2 | -1 | 0 | 1 | 2 | 3 y | 4 | 0 | -2 | -2 | 0 | 4 Why: a parabola is a smooth curve, not a set of straight segments, so the points are joined freehand with one curve. The values y=-2 at x=0 and x=1 are equal, so the turning point lies halfway between them, at x=0.5, slightly below the lowest plotted points: y=0.25-0.5-2=-2.25. Method - Complete the table by substituting each x-value, working out x2 first and keeping signs. - Draw the axes with the scale stated in the question, for example 2 cm to 1 unit on the x-axis and 1 cm to 1 unit on the y-axis. - Plot every point, then draw one smooth curve through them, rounding off the bottom (or top) between the two lowest (or highest) points. - To read a value, draw a line from the axis to the curve and across to the other axis, and give the answer to the accuracy the scale allows. - When a<0 the curve is upside down: round off the top between the two highest points; the turning point is a maximum. - If no two plotted y-values are equal, the turning point is not a plotted point: read it from the smooth curve, and use two points with equal y-values on the curve for the line of symmetry. Example From the graph of y=x2-x-2, when x=2.5 the dashed lines give y=1.75. The line of symmetry is x=0.5, and the minimum point is (0.5,-2.25). To find x for a given y, draw the horizontal line. The dashed line y=1 meets the curve twice, at x -1.3 and x 2.3; give both values. Check: substitute x=2.5: 6.25-2.5-2=1.75, and 2.32-2.3-2=0.99 1. A common error is to join the two lowest points with a flat line; the curve dips below them to the turning point.

Drawing a quadratic graph from a table

Secondary 2

To draw the graph of a quadratic function accurately, work out a table of values, choose a scale for each axis, plot the points and join them with a smooth curve.

Table for $y=x^2-x-2$

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

Why: a parabola is a smooth curve, not a set of straight segments, so the points are joined freehand with one curve. The values $y=-2$ at $x=0$ and $x=1$ are equal, so the turning point lies halfway between them, at $x=0.5$, slightly below the lowest plotted points: $y=0.25-0.5-2=-2.25$.

Method

Complete the table by substituting each $x$-value, working out $x^2$ first and keeping signs.
Draw the axes with the scale stated in the question, for example $2$ cm to $1$ unit on the $x$-axis and $1$ cm to $1$ unit on the $y$-axis.
Plot every point, then draw one smooth curve through them, rounding off the bottom (or top) between the two lowest (or highest) points.
To read a value, draw a line from the axis to the curve and across to the other axis, and give the answer to the accuracy the scale allows.
When $a<0$ the curve is upside down: round off the top between the two highest points; the turning point is a maximum.
If no two plotted $y$-values are equal, the turning point is not a plotted point: read it from the smooth curve, and use two points with equal $y$-values on the curve for the line of symmetry.

Example

From the graph of $y=x^2-x-2$, when $x=2.5$ the dashed lines give $y=1.75$. The line of symmetry is $x=0.5$, and the minimum point is $(0.5,-2.25)$.

To find $x$ for a given $y$, draw the horizontal line. The dashed line $y=1$ meets the curve twice, at $x\approx-1.3$ and $x\approx2.3$; give both values.

Check: substitute $x=2.5$: $6.25-2.5-2=1.75$, and $2.3^2-2.3-2=0.99\approx1$. A common error is to join the two lowest points with a flat line; the curve dips below them to the turning point.

Create a free account to practise similar questions.

Create free account Sign in Get the E Math course · from S$29.98/mo E Math tuition

Need help? Join our E-Maths tuition for O-Level success.

Learn more