Explain the connections between quadratic functions and quadratic equations that

Question

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.

Answer 1

Step 1
Part (a)
Let quadratic function $f (x)$
Let qusdratic equation $f (x) = 0$
For solution of 2 and 6
$∴$ quadratic fynction
$f (x) = (x - 2) (x - 6)$
$= x^{2} - 6 x - 2 x + 12$
$f (x) = x^{2} - 8 x + 12$
And quadratic equation
$f (x) = 0$
$x^{2} - 8 x + 12 = 0$
Step 2
Part (b)
$∴$ Solutions of a quadratic equation are 2 and 6
$∴ {equation}^{n} : (x - 2) (x - 6) = 0$
$= x^{2} - 8 x + 12 = 0$
And function:
$y = x^{2} - 8 x + 12$
Zeroes of function are $x = 2 and x = 6$
$\begin{array}{cc} x & 1 & 0 & 2 & - 2 & 3 & 6 \\ y & 5 & 12 & 0 & 32 & - 3 & 0 \end{array}$

Explain the connections between quadratic functions and quadratic equations that

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