Question

2 Find the vertex of the function and identify it as a maximum or a minimum

Answer 1

(-2, 5) Minimum

Step-by-step explanation:

y-5=(1/3)(x + 2)²

y-5=(1/3)(x²+4x+4))

y-5=1/3x²+4/3x+4/3

y=1/3x²+4/3x+4/3+5

y=1/3x²+4/3x+4/3+15/3

y=1/3x²+4/3x+19/3

graph is attached

x= -b/2a

x= (-4/3)/2(1/3)

x= (-4/3)/(2/3)

x= (-4/3)*(3/2)

3's cancel

x= (-4/1)*(1/2)

x = -4/2

x = -2

plug -2 back into

y=1/3x²+4/3x+19/3

y=1/3*4+4/3*-2+19/3

y=4/3-8/3+19/3

y=15/3

y=5

(-2,5)

if a is positive

graph looks like a smile

so minimum

if a is negative

graph looks like a frown

so maximum

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