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6.03 Graphical approach to solving equations

Interactive practice questions

Consider the function $f(x)=\left|2x+4\right|$f(x)=|2x+4|.

a

The graph of the function is given. On the same set of axes, plot the points at which $f(x)=2$f(x)=2.

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b

How many solutions does the equation $\left|2x+4\right|=2$|2x+4|=2 have?

c

Using the result of part (a) or otherwise, find the solutions to the equation $\left|2x+4\right|=2$|2x+4|=2.

State your solutions on the same line, separated by a comma.

Easy
3min

Consider the equation $\left|5x\right|=15$|5x|=15.

Easy
1min

The cubic function $y=\left(x+1\right)\left(x-2\right)\left(x-3\right)$y=(x+1)(x2)(x3) has been graphed.

Determine the number of solutions to the equation $\left(x+1\right)\left(x-2\right)\left(x-3\right)=0$(x+1)(x2)(x3)=0.

Easy
< 1min

Consider the equations $y=x^2$y=x2 and $y=9$y=9.

Easy
2min
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Outcomes

MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

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