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jholland03
29.09.2019 •
Mathematics
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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=
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Ответ:
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=2a*11+b ==> b=-22a (2)
(1) and (2)==>a+22a+c=2 ==>23a+c=2 (3)
The parabola is passing through (11,-9)
-9=a*121+11*b+c (4)
(4) and (2)==> a*121+11*(-22a)+c=-9 ==>-121a+c=-9 (5)
(3)-(5)==>144 a=11==>a=11/144
(2)==>b=-22*11/144==>b=-242/144
(3)==>c=2-23*11/144==>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
Ответ:
1 square inch. = 1.2732 circular inches. Volume. 1728 c
Step-by-step explanation:
ubic inches. = 1 cubic foot. 27 cubic feet ... When water is at its maximum density, 1 cubic foot weighs 62.428 ... Weight. 10 milligrams (mg.) = 1 centigram. 10 centigrams (cg.) = 1 decigram ... DECIMAL EQUIVALENTS OF PARTS OF AN INCH. 1/64 . =015625. 33/64.