SOLUTION: Line t is parallel to the line y=3x+2 and passes thru the highest point on the graph of y=x(10-x). What is the equation of t? Thankyou for your help

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Question 140452: Line t is parallel to the line y=3x+2 and passes thru the highest point on the graph of y=x(10-x). What is the equation of t?

Thankyou for your help
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
parallel means same slope, so y=3x+b

the highest point of the graph is the vertex, which is on the axis of symmetry

y=x(10-x) __ y=-x^2+10x
__ for axis of symmetry, x=-b/2a __ x=-10/(-2) __ x=5

substituting __ y=5(10-5) __ y=25

substituting __ 25=3(5)+b __ 25=15+b __ 10=b

so t is y=3x+10