1) Graph the quadratic function given in standard form and identify the key features. Include at least 5 points on your graph.
y = -x2 - 2x + 1
Axis of Symmetry:
Vertex:
Y-intercept:
Domain:
Range:

Please find attached the graph of the quadratic function is created using Microsoft Excel

1) The line of symmetry is x = -1

2) The vertex is (-1, 2)

3) The y-intercept is (0, 1)

4) The domain is -∞ ≤ x ≤ ∞

5) The range is 2 ≥ y ≥ -∞

Step-by-step explanation:

The given equation is y = -x² - 2·x + 1

The general vertex form is y = a·(x - h)² + k

h = -b/(2·a) = 2/(-2) = -1

k = f(h) = -(-1)² - 2×(-1) + 1 = 2

Therefore;

1) The line of symmetry goes through the vertex and the line of symmetry is x = -1

2) The vertex = (h, k) = (-1, 2)

3) The y-intercept is the coordinate of the point where x = 0 which is  (0, 1)

4) The domain are the possible x-values, therefore, the domain = -∞ ≤ x ≤ ∞

5) The range is the possible values y-values.

From the graph, we have the range = 2 ≥ y ≥ -∞

The graph of the quadratic function is created using Microsoft Excel by generating y-values based on the equation and using the graphing function to insert a two dimensional graph of the generated combination of x and y values as shown in the attached figure.

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