Question 1190538
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Find the quadratic function y=a(x−h)2 whose graph passes through the given points.
​(4​,−2​) and ​(2​,0)
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<pre>
Let's consider the point (2,0) first.


The fact that it belongs to the given form parabola MEANS that

    0 = a*(2-h)^2


which, with a=/=0, IMPLIES  h= 2.


So, half of the problem is just solved, and we know that h= 2.


THEREFORE, we can re-write the quadratic function in the form

    y = a*(x-2)^2.



Now consider the second point, (4,-2).


The fact that it belongs to the given form parabola MEANS that

    -2 = a*(4-2)^2,   or   -2 = a*2^2,    or   -2 = 4a


which implies  a= {{{(-2)/4}}} = -0.5.


So, the quadratic function is  y = -0.5*(x-2)^2,   and  h= 2, a= -0.5.    <U>ANSWER</U>
</pre>

Solved.