Answer:
Step-by-step explanation:
f(x) = x2 + 2x - 2 should be rewritten using " ^ " to indicate exponentiation:
f(x) = x^2 + 2x - 2.
We find a couple of key points and use the fact that this parabola is symmetric about the line
-2
x = ----------- = -1. When x = -1, y = f(-1) = (-1)^2 + 2(-1) - 2, or 1 - 2 -2, or -3.
2(1)
Thus the vertex is at (-1, -3). The y-intercept is found by letting x = 0: y = -2. The axis of symmetry is x = -1.
Graph x = -1 and then reflect this y-intercept (0, -2) about the line x = -1, obtaining (-2, -2). If necessary, find 1 or two more points (such as the x-intercepts).
To find the roots (x-intercepts), set f(x) = x^2 + 2x - 2 = 0 and solve for x.
Completing the square, we obtain x^2 + 2x + 1 - 2 = + 1, or (x + 1)^2 = 3.
Taking the square root of both sides yields x + 1 = ±√3. One of the two roots is x = 1.732 - 1, or 0.732, so one of the two x-intercepts is (0.732, 0).
Answer:
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that , or equivalently, and .
If and , we just need to substitute known values and solve for k:
Double checking that k works for the y-coordinates as well:
?
So,
Answer:
The numbers are and
The graph in the attached figure
Step-by-step explanation:
we know that
To find the first number, adds 6 units to the number 2 and to find the second number subtract 6 units from the number 2
Let
x-----> the first number
y-----> the second number
we have
using a graphing tool
see the attached figure
2+1=3 is not an identity property. The rest are because the value equals itself after dividing, subtracting, and multiplying.
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