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(-1, -9/2) minimum true

1/2 (x+1)^2 -9/2 is the vertex form  false

the axis of symmetry is at the x value of the vertex  x=-1  false

The parabola opens up since the x^2 coefficient is positive false

x=-4    x=2  true

Step-by-step explanation:

f(x) = 1/2x^2 +x - 4

Factor out 1/2

f(x) = 1/2 (x^2 +2x - 8)

Factor

f(x) = 1/2 ( x+4)(x-2)

Finding the zeros

0= 1/2 ( x+4)(x-2)

Using the zero product property

x+4 = 0   x-2=0

x=-4    x=2

The vertex is 1/2 way between the zeros

(-4+2)/2 = -2/2 = -1

f(-1) = 1/2 (-1+4) (-1-2) = 1/2(3)(-3) =-9/2

The vertex is (-1, -9/2)

The parabola opens up since the x^2 coefficient is positive so this is the minimum

f(x) = 1/2 (x+1)^2 -9/2 is the vertex form

the axis of symmetry is at the x value of the vertex  x=-1