The book is Precalculus A Right Triangle Approach 3rd Ed In

The book is Precalculus A Right Triangle Approach, 3^rd Ed. In Exercies 35-40, the graphs of y=ax²+bx+c are given. Find the signs of a, b, and c and state which (if any) are zero.

Solution

In the question no graph is attached

Given y=ax^2+bx+c

so, dy/dx=2ax+b

for maximum or minimum dy/dx=0

=> 2ax+b=0

=> x=-b/(2a)

d^2y/dx^2=2a

Case 1:-so now it depends on graph if graph is concave up that is minimum then d^2y/dx^2 is positive

that means \'a\' will be positive

Case 2:- if graph is concave down that is maximum then d^2y/dx^2 is negative

that means \'a\' will be negative

x=-b/2a where there is maximum or minimum point we can find by putting the value of \'a\'

then we will find the value of roots ten value of \'c\' accordingly