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Find values of a, band cso that the graph of the polynomial p(x)=ax2+bx+cpasses through the point (−1,2)and has a horizontal tangent at (11,−9).

(Do not convert fractions to decimals in your answers, enter them exactly e.g. 11/27, 1/3 etc.) (Hint: form a linear system based on the assumptions and solve it using your favourite method. See your lectures notes on applications of linear systems.)

a= ____________

b= ____________

c= ____________

Verified Answer :

caylus

Hello,

y=ax²+bx+c

Method 1:

The parabola is passing through (-1,2)
==>2=a-b+c (1)
The parabola has a horizontal tangent  at(11,-9)

y'=2ax+b
==>0=2a11+b ==> b=-22a (2)
(1) and (2)==>a+22a+c=2 ==>23a+c=2 (3)

The parabola is passing through (11,-9)
-9=a121+11b+c (4)
(4) and (2)==> a121+11(-22a)+c=-9 ==>-121a+c=-9 (5)

(3)-(5)==>144 a=11==>a=11/144
(2)==>b=-2211/144==>b=-242/144
(3)==>c=2-2311/144==>c=35/144



Method 2

The vertex is (11,-9) and the parabola is passing through (-1,2)

y=k(x-11)²-9
2=k(-12)²-9==>k=11/144
The equation is : y=11/144(x-11)²-9 ==>y=11/142x²-242/144x+35/144






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