Answer:
(-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
