Mathematics 0580 · IGCSE · Graphs of functions

Graphs of functions — practice question

The table presents some values for $y = x^3 + 3x^2 + 2$. The listed $x$-values are $-3.5, -3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5$, and the matching $y$-entries are only partly filled in.
(a)[3]

Finish the table.

(b)[4]

On the grid, sketch the graph of $y = x^3 + 3x^2 + 2$ for $-3.5 \le x \le 1.5$.

(c)[1]

Use your graph to solve $x^3 + 3x^2 + 2 = 0$ for $-3.5 \le x \le 1.5$.

(d)[2]

By plotting a suitable straight line, solve $x^3 + 3x^2 + 2x + 2 = 0$ for $-3.5 \le x \le 1.5$.

(e)[1]

For $-3.5 \le x \le 1.5$, the equation $x^3 + 3x^2 + 2 = k$ has three solutions, and $k$ is an integer. Write down one possible value of $k$.

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