Mathematics, 30.08.2019 23:00 mdlemuslopez

For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.

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Vertex form is a(x-h)^2+k. The vertex is (h,k), and you basically take the opposite of h and you copy down k. For example, if the vertex of a parabola is represented by 2(x+2)^2-6, (-2,-6) would be the vertex. Also, the domain is the interval at which the x-values are extended, and the interval at which the y-values are extended would be the range. In order to identify these aspects of the function, work backwards to get the starting quadratic that this function was represented as. Then, if the function is just a quadratic polynomial, then a rule is that the domain and range of the function are all real numbers, as there isn't a denominator of the function to worry about (different steps will be taken for that). You can express the domain and range as two separate ordered pairs, such as domain- (how far left the function will go, how far right the function will go) and range- (how far down the function will go, how far up the function will go).

Answer from: Quest

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

Answer from: Quest

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~

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For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range....