Question

find the vertex line of symmetry and maximum or minimum of f(x). Graph the function f(x)=-5(x+3)^2+3

Answer 1

calc? or no clac?

Answer 2

no

Answer 3

y` = -10(x+3)
y`=0=-10x-30
-10x=30
x = -3 is line of symmetry
f(-3) = 3 is critical point
to see if its a min or max take second derv
-10 thus a max

Answer 4

oh

Answer 5

do you know how to find vertex?

Answer 6

NO

Answer 7

-5(x+3)^2+3
-5(x^2+6x+9)+3
-5x^2-30x+12
vertex is -b/2a so 30/-10 = -3
f(-3) = 3 this isthe x cordinate of the peak or valley of the paraballa. The fact that the 1st term is negative means it opens down so we know....
x= -3 is the line of symetry and f(-3)=3 or (-3,3) is a maximum

Answer 8

calculus was one line faster:)

Answer 9

Thank you so much for explaining, I am struggling

Answer 10

-5(x+3)^2+3
-5(x^2+6x+9)+3
-5x^2-30x-42
vertex is -b/2a so 30/-10 = -3
f(-3) = 3 this isthe x cordinate of the peak or valley of the paraballa. The fact that the 1st term is negative means it opens down so we know....
x= -3 is the line of symetry and f(-3)=3 or (-3,3) is a maximum

Answer 11

small typo sorry does not change answer.