Question

find a parabola y=ax^2 + bx + c that passes through the point ( 1, 4 ) and whose tangent lines at x=-1 and x=5 have slopes of 6 and -2 respectively.

Answer 1

HI!!

Answer 2

we gotta make some equations

Answer 3

first one says
\[4=a+b+c\]

Answer 4

the derivative is
\[2ax+b\] so the second one says
\[-2a+b=6\]

Answer 5

third one says
\[10a+b=-2\]

Answer 6

solve the system
\[-2a+b=6\\
10a+b=-2\] for \(a\) and\(b\), then replace in the first one to find \(c\)

Answer 7

how did you get 10a + b = -2?