4 Quadratics and polynomials

Consider the equation $y=x\left(x-4\right)$`y`=`x`(`x`−4).

a

Determine the $y$`y`-value of the $y$`y`-intercept of the graph.

b

Determine the $x$`x`-values of the $x$`x`-intercepts. Write all solutions on the same line separated by a comma.

c

Complete the table of values for the equation.

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

$y$y |
$\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |

d

Determine the coordinates of the turning point of the parabola. State your answer in the form $\left(a,b\right)$(`a`,`b`).

e

Plot the graph of the parabola.

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Easy

Approx 6 minutes

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Explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate