Question 1190538
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The equation is {{{y=a(x-h)^2}}}, which is equivalent to {{{y=a(x-h)^2+0}}}; the vertical shift is 0, so the vertex is on the x-axis.<br>
One of the given points is (2,0), which is on the x-axis, so (2,0) is the vertex.<br>
The other given point is below the x-axis, so the graph opens downward; the leading coefficient "a" is negative.<br>
To determine the leading coefficient, we can use formal mathematics as the other tutor did; but we can find it informally, as follows:<br>
The second point given is 2 units to the right of the vertex.  If the leading coefficient were -1, the y coordinate of that second point would be -(2^2) = -4; but it is only -2.  That means the leading coefficient is -1/2 instead of -1.<br>
So a=-1/2 and h=2.<br>
ANSWER: {{{y=(-1/2)(x-2)^2}}}<br>