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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+2x%5E2-6x%2B3
You have correctly found the x-coordinate of the vertex:
x+=+3%2F2 and you have made a start on finding the corresponding y-coordinate by substituting x+=+3%2F2 into the given quadratic equation to solve for y.
y+=+2%283%2F2%29%5E2-6%283%2F2%29%2B3 Simplify.
y+=+2%289%2F4%29-6%283%2F2%29%2B3
y+=+9%2F2-18%2F2%2B6%2F2
y+=+-3%2F2
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 x%5E2 term.
The axis of symmetry is give by x+=+3%2F2 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 y+=+-3%2F2 it is clear that the range is -3%2F2 and above.
So the range can be written as:
y%3E=-3%2F2
You can see this from the graph:
graph%28400%2C400%2C-5%2C5%2C-3%2C10%2C2x%5E2-6x%2B3%29

Answer by Theo(13342) About Me  (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:
graph%28600%2C600%2C-5%2C5%2C-3%2C3%2C2x%5E2-6x%2B3%2C-3%2F2%29
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.