Functions 1 and 2 are shown below: function 1: f(x) = −3x2 + 2 a graph of a parabola with x intercepts of negative 0.5, 0 and 2, 0 and a vertex of 0.5, 4 is shown. which function has a larger maximum? type your answer as 1 or 2.

The maximum value of function 1 is 2 and  maximum value of function 2 is 4. So, function 2 has a larger maximum.

Step-by-step explanation:

In Function 1 :

Lending coefficient is negative. It is a downward parabola and vertex is the maximum point.

vertex of a parabola is

On comparing with given equation we ave;

a = -3 , b=0 and c = 2

then;

Substitute the value of x =0 in we have;

⇒Vertex = (0, 2)

⇒the maximum value of function 1 is 2.

In Function 2:

Vertex = (0.5, 4)

⇒the maximum value of function 2 is 4.

Therefore, Function 2 has a larger maximum.

n

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12