```Question 542528
equation is:
y = 2x^2 - 6x + 3
x value of min/max point is given by the equation x = -b/2a
a = 2
b = -6
c = 3
you were on the right track.
x = 3/2
substitute for x in the equation to get y = -3/2
your min/max point is (x,y) = (3/2,-3/2)
since the coefficient of the x^2 term is positive, then this is a min point.
the axis of symmetry is the line x = 3/2.
the domain of the parabola is x equal the set of all real numbers.
the range of the parabola is y equal the set of all real number >= -3/2
a graph of your equation is shown below:
{{{graph(600,600,-5,5,-3,3,2x^2-6x+3,-3/2)}}}
the value of x has no restrictions which is why we say the domain the equation equals the set of all real numbers.
the value of y will never go below -3/2 but can go as high as it wants to based on the value of x which is why we say the range is equal to the set of all real numbers greater than or equal to -3/2.
a horizontal line was drawn at -3/2 to show you that it is the minimum value that that the equation can generate.```