SOLUTION: The point A lies on the parabola y=x^2 - 6x +24. The point B lies on the parabola y= 6x-x^2 and is vertically below the point A. a) Show this information on a neat diagram b) Fin

Algebra ->  Linear-equations -> SOLUTION: The point A lies on the parabola y=x^2 - 6x +24. The point B lies on the parabola y= 6x-x^2 and is vertically below the point A. a) Show this information on a neat diagram b) Fin      Log On


   

Question 1128589: The point A lies on the parabola y=x^2 - 6x +24. The point B lies on the parabola y= 6x-x^2 and is vertically below the point A.
a) Show this information on a neat diagram
b) Find the least value of the length of line AB
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The point A lies on the parabola
y=x%5E2+-+6x+%2B24
The point B lies on the parabola y=+6x-x%5E2 and is vertically+below+the point+A.
solution:
y=x%5E2+-+6x+%2B24 -> parabola is opening+up, the point A in vertex (minimum)
y=+-x%5E2%2B6x -> parabola is opening+down, the point B in vertex (maximum)

writ both equations in vertex form:
y=%28x%5E2+-+6x%29+%2B24
y=%28x%5E2+-+6x%2Bb%5E2%29+-b%5E2%2B24
y=%28x%5E2+-+6x%2B3%5E2%29+-3%5E2%2B24
y=%28x+-+3%29%5E2+-9%2B24
y=%28x+-+3%29%5E2+%2B15
=> vertex is at (3,15)=>the point A+

y=+-x%5E2%2B6x
y=+-%28x%5E2-6x%2Bb%5E2%29-1%28-b%5E2%29
y=+-%28x%5E2-6x%2B3%5E2%29-1%28-3%5E2%29
y=+-%28x-3%29%5E2%2B9
=> vertex is at (3,9)=>the point B
since both points have same x coordinate, the point B lies vertically below the point A because y coordinate of the point A is greater than y coordinate of the point B


a) Show this information on a neat diagram



b) Find the least value of the length of line AB
the length of line AB=15-9=6