The equation 4x^2+8x+15=0 is being rewritten in vertex form

Vertex form is y = (2x+2)^2 + 7  

Step-by-step explanation:

The vertex form is

y = (x-h)^2+k

Where (h,k) is the vertex.

Let

y = 4x^2 + 8x +15

Add -15 on both sides

y-15 = 4x^2+8x+15 -15

y-15 = 4x^2+8x

Making whole square formula on Right hand side (a+b)^2

(2x)^2 + 2(2x)(2)+(2)^2 = (2x+2)^2

Adding (2)^2 on both sides of the equation

y-15+(2)^2=4x^2+8x+(2)^2

y-15+4=(2x+2)^2

y-7 = (2x+2)^2

y = (2x+2)^2 + 7

So, Vertex form is y = (2x+2)^2 + 7  

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

.25

step-by-step explanation: