SOLUTION: can you please help me determine how many x-intercepts the parabola has and wether its vertex lies above or below or on the x-axis ((( y=x^2-5x+6 ))) {{{y=x^2-5x+6}}}------(1)

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: can you please help me determine how many x-intercepts the parabola has and wether its vertex lies above or below or on the x-axis ((( y=x^2-5x+6 ))) {{{y=x^2-5x+6}}}------(1)       Log On


   



Question 198266This question is from textbook algebra sturcture and method
: can you please help me determine how many x-intercepts the parabola has and wether its vertex lies above or below or on the x-axis ((( y=x^2-5x+6 )))
y=x%5E2-5x%2B6------(1)
x intercept ==> y=0. So put y=0 in (1)
==> x%5E2-5x%2B6=0
==> %28x-3%29%28x-2%29=0
==> x={2,3}
So the parabola have two x intercepts.
Since the sign of x^2 is positive, the parabola has a minimum at its vertex.
Vertex is [-b/2a,f(-b/2a)]= (5/2,-1/4) So the vertex lies below the x axis.
This question is from textbook algebra sturcture and method

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