In the first step, you match the pattern of
.. (-3/2)x^2 +0x +3
to the pattern of
.. ax^2 +bx +c
and you can see that
.. a = -3/2 . . . b = 0 . . . c = 3
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Because a is negative, the parabola opens down. Because it opens down, the vertex is the high point, the maximum.
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The y-intercept is always c. Here c=3, so the y-intercept is (0, 3).
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The axis of symmetry is given by
.. x = -b/(2a)
.. x = -0/(2*(-3/2)) = 0
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Because the y-intercept is on the axis of symmetry, it is the vertex.
.. vertex = (0, 3)
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Put x=±2 in the equation and evaluate.
.. y = (-3/2)*(±2)^2 +3
.. = (-3/2)*4 +3
.. = -6 +3 = -3
The two points are (-2, -3) and (2, -3).
