SOLUTION: Problem. Identify the axis of symmetry, create a suitable table of values and sketch the graph. The problem is y=x^2-5x+3. I've identified the axis of symmetry as 5/2 but I am h

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Problem. Identify the axis of symmetry, create a suitable table of values and sketch the graph. The problem is y=x^2-5x+3. I've identified the axis of symmetry as 5/2 but I am h      Log On


   

Question 105586: Problem. Identify the axis of symmetry, create a suitable table of values and sketch the graph. The problem is y=x^2-5x+3. I've identified the axis of symmetry as 5/2 but I am having difficulty creating the table of values. Any assistance would be greatly appreciated.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-5x%2B3
the axis of symmetry is 5%2F2 draw the line perpendicular on x-axis passing thruogh this point

table:
x|y
0|3 _________ ifx=0 => theny+=0%5E2-5%2A0%2B3 => y=3
1|-1 _________ ifx=1 => theny+=1%5E2-5%2A1%2B3 => y=-1
2|-3 _________ ifx=2 => theny+=2%5E2-5%2A2%2B3 => y=-3
:
:
:and so on


Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A1%2A3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+4.30277563773199
x%5B2%5D+=+%28-%28-5%29-sqrt%28+13+%29%29%2F2%5C1+=+0.697224362268005

Quadratic expression 1x%5E2%2B-5x%2B3 can be factored:
1x%5E2%2B-5x%2B3+=+%28x-4.30277563773199%29%2A%28x-0.697224362268005%29
Again, the answer is: 4.30277563773199, 0.697224362268005. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B3+%29