Drawing Graphs from Tables Flashcards

All 8 cards in this deck

What are the steps to find a missing $y$-value in a table of values for a quadratic?

e.g. $y = x^2 - x - 2$ when $x = -2$

1. Substitute the $x$-value: $(-2)^2 - (-2) - 2$.
2. Work out the power first: $4 + 2 - 2$.
3. Add and subtract: $y = 4$.

What are the steps to draw a graph from a completed table of values?

e.g. $y = x^2 - x - 2$ for $x$ from $-2$ to $3$

1. Plot each $(x, y)$ pair from the table as a point.
2. Join them with a single smooth freehand curve, not straight line segments.
3. Keep the curve within the given range, $x = -2$ to $x = 3$.

A student draws the graph of $y = x^2 + 1$ by joining her plotted points with a ruler. What is wrong with her graph?

It is made of straight line segments — it should be a smooth curve drawn freehand.

How do you complete a table of values for a reciprocal function $y = \frac{k}{x}$?

e.g. $y = \frac{6}{x}$ when $x = 0.5$

Divide $k$ by each $x$-value.

$6 \div 0.5 = 12$, so $y = 12$.

Which value of $x$ can never appear in a table of values for $y = \frac{k}{x}$?

$x = 0$ — you cannot divide by zero, so the graph has no point there.

When drawing a graph from a completed table of values, what does each column of the table give you?

e.g. the column $x = -2$, $y = 4$

One coordinate pair to plot.

e.g. plot the point $(-2, 4)$.

Two neighbouring points in a quadratic table have the same lowest $y$-value. Where should the curve go between them?

e.g. $y = -2$ at both $x = 0$ and $x = 1$

It should dip below them, reaching its minimum halfway between the two $x$-values.

e.g. the lowest point is below $y = -2$, at $x = 0.5$.

True or false? A curve drawn from a table of values is acceptable as long as it passes close to the plotted points.

False. The curve must pass through every plotted point.