Answer:
A: -4
B: 4
C: m(x)<h(x) for every x, t.e m(x)>h(x) cann’t be treu for any value of x.
Step-by-step explanation:
I’m not sure what is fubction m. I will suppose it is linear function.
For example m(x)=x/2-2.
Part A: h(4)-m(16)=1/2(4-2)^2 - 16/2-2=2-6=-4
Part B: y-intersection on h(x), we find how is h(0). So h(0)=1/2(0-2)^2=2.
For m(x), m(0)=0/2-2=-2. So their y-intersections are fare away 4. (See photo)
Part C: First we chak if there any intersection between h and m.
1/2(x-2)^2=x/2-2, si we have
x^2-4x+4-x+4=0
X^2-5x+8=0,
D=5^2-4*8=25-32<0, so m and h don’t have intersection, and from graph we can see that for every value of x, m(x) will always be less than h(x).
Photo: blue is h(x), green is m(x)
