Explain the connections between quadratic functions and quadratic equations that contains the following:
a) A representative function for a quadratic equation with solutions of 2 and 6.
b) A table of ordered pairs of a representative function for a quadratic equation with solutions of 2 and 6, with the zeros of the function included and circled.
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Step 1
Part (a)
Let quadratic function $f\left(x\right)$
Let qusdratic equation $f\left(x\right)=0$
For solution of 2 and 6
$\therefore$ quadratic fynction
$f\left(x\right)=\left(x-2\right)\left(x-6\right)$
$={x}^{2}-6x-2x+12$
$f\left(x\right)={x}^{2}-8x+12$
$f\left(x\right)=0$
${x}^{2}-8x+12=0$
Step 2
Part (b)
$\therefore$ Solutions of a quadratic equation are 2 and 6

$={x}^{2}-8x+12=0$
And function:
$y={x}^{2}-8x+12$
Zeroes of function are
$\begin{array}{|ccccccc|}\hline x& 1& 0& 2& -2& 3& 6\\ y& 5& 12& 0& 32& -3& 0\\ \hline\end{array}$