(a) Show that the quadratic function f(r) = ax² + br+c is concave up if a > 0 and is concavedown if a < 0. Therefore, the rule that a parabola opens up if a > 0 and down if a < 0 ismerely an application of concavity.(b) The concentration of a drug in a patient's bloodstream t hours after it is injected is givenby0.05tC(t) =t2 + 27milligrams per cubic centimeter.i. Sketch the graph of the concentration function by describing all the possible detailsneeded to plot it.ii. At what time is the concentration decreasing most rapidly?iii. What happens to the concentration in the long run?

NOTE- AS WE ARE ALLOWED TO ANSWER ONE QUESTION IN ONE SESSION SO, I HAVE ANSWERED FIRST QUESTION FOR…

(a) Show that the quadratic function f(r) = ax² + bx+c is concave up if a > 0 and is concave down if a < 0. Therefore, the rule that a parabola opens up if a > 0 and down if a < 0 is merely an application of concavity.

(a) Show that the quadratic function f(r) = ax² + bx+c is concave up if a > 0 and is concave down if a < 0. Therefore, the rule that a parabola opens up if a > 0 and down if a < 0 is merely an application of concavity.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.2: Transformations Of Quadratic Functions

Problem 50PFA

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Question

(a) Show that the quadratic function f(r) = ax² + br+c is concave up if a > 0 and is concave
down if a < 0. Therefore, the rule that a parabola opens up if a > 0 and down if a < 0 is
merely an application of concavity.
(b) The concentration of a drug in a patient's bloodstream t hours after it is injected is given
by
0.05t
C(t) =
t2 + 27
milligrams per cubic centimeter.
i. Sketch the graph of the concentration function by describing all the possible details
needed to plot it.
ii. At what time is the concentration decreasing most rapidly?
iii. What happens to the concentration in the long run?

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