Question

0. Which best describes the graph of the polynomial function
f(x) = x2 + 2x - 15? with solution​

Answer 1

Given  : f(x) = x²  + 2x - 15

To Find : describes the graph

Solution:

f(x) = x²  + 2x - 15

=> f(x) = x²  + 5x -3x-  15

=> f(x) = x(x + 5)  -3(x + 5)

=> f(x) = (x + 5)(x  -3)

Graph will cut the x axis at x = - 5   & x = 3

x > 3  , x < - 5

f(x) = +ve  > 0

-5 < x  < 3

=> f(x) = -ve  < 0

Hence Graph will be upward

f(x) = x² + 2x - 15

=> f'(x) = 2x + 2

=> x = - 1

f''(x) = 2 > 0

hence x  = - 1  will give minimum value of the graph

or directly  ( 3 - 5)/2 = - 1  will give minimum value of the graph

f(-1) =  -16  

Graph will be symmetric around  x  = - 1

with lowest value = - 16

Graph will be upward

cut x axis at x = 3 , - 5  

cut y axis at  ( 0 , - 15)

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