SOLUTION: can you please help me solve the following: (((How many x-intercepts the parabola has and wheather its vertex lies above or below or on the x-axis, y=x^2-5x+6)))

Algebra ->  Expressions-with-variables -> SOLUTION: can you please help me solve the following: (((How many x-intercepts the parabola has and wheather its vertex lies above or below or on the x-axis, y=x^2-5x+6)))      Log On


   

Question 180347This question is from textbook algebra structure and method
: can you please help me solve the following: (((How many x-intercepts the parabola has and wheather its vertex lies above or below or on the x-axis, y=x^2-5x+6))) This question is from textbook algebra structure and method

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
set y = to zero when trying to find the x intercepts
:
x%5E2-5x%2B6=0
:
%28x-2%29%28x-3%29=0
:
x=2 and 3
:
since this has two intercepts we know that the vertex is NOT on the x axis
:
we also know that this parabola opens up(coefficent is positive in x squared term) therefore we know the vertex is below the x axis, but not by much because the x intercepts are very close to each other
:
we can find the exact vertex by completing the square
:
y=x%5E2-5x%2B%2825%2F4%29%296-25%2F4
:
y=%28x-%285%2F2%29%29%5E2-%281%2F4%29
:
so the vertex is at (5/2,-1/4)
:
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E2-5x%2B6%29