Question 1209609
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Answer: Anything of the form {{{y = a(x-2)(x+2)}}} where 'a' is a real number
One example is {{{y = 5(x-2)(x+2)}}} where a = 5.


Explanation


If the quadratic has x = 2 as a root, then x-2 = 0. This leads to (x-2) as a factor.
x = -2 as a root leads to (x+2) as a factor.


That explains the {{{(x-2)(x+2)}}} portion.


It changes to {{{a(x-2)(x+2)}}} so we can vertically stretch and compress the parabola.


Check out this Desmos graph.
<a href="https://www.desmos.com/calculator/bzmy0reizl">https://www.desmos.com/calculator/bzmy0reizl</a>
Move the slider around for parameter 'a' so you can see these changes.


Notes:<ul><li>When a < 0, the parabola opens downward.</li><li>When a > 0, the parabola opens upward.</li><li>When a = 0, the graph is a flat horizontal line overlapping the x axis.</li><li>The portion "takes the value 0 when x = 2" is redundant since x = 2 is a root aka x intercept.</ul></font>