SOLUTION: I have to find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. the formula is y=ax^2+bx+c Question: y=2x^2-6x+3 What i have so far: y=2x^2-6x

Question 542528: I have to find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. the formula is y=ax^2+bx+c
Question: y=2x^2-6x+3
What i have so far:
y=2x^2-6x+3
-b/2a=-(-6)/2(2)=6/4=3/2
y=2(3/2)^2-6(3/2)+3
2(9/4)-(-18)/2
I am stuck, I'm not sure if im doing it right but if you could help explain it to me that would be awsome! thank you!
Found 2 solutions by Earlsdon, Theo:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!

You have correctly found the x-coordinate of the vertex:
and you have made a start on finding the corresponding y-coordinate by substituting into the given quadratic equation to solve for y.
Simplify.

The coordinates of the vertex are: (3/2, -3/2)
The vertex is a minimum (the parabola opens upward) which is indicated by the positive coefficient of the term.
The axis of symmetry is give by which is the equation of the vertical line passing through the point (3/2, -3/2). (the vertex.)
The range consists of all of the valid y-values.
Since the y=coordinate of the vertex (a minimum) is it is clear that the range is and above.
So the range can be written as:

You can see this from the graph:

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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:

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.
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