The lines shown below are parallel. If the green line has a slope of 5, what is a
2 answers:
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The vertex form of the given quadratic equation is
.
According to the given question.
We have a quadratic equation
Since, for the standard quadratic form is , the vertex form of a quadratic equation is
where (h, k) is the vertex.
And h and k can be calculated as
h = -b/2a and y = k
So, for the given equation the vertex (h, k) is given by
h = -(-8)/2(4) = 8/8 = 1 (X coordinate of vertex)
and,
substitute x = 1 in the above equation for the value of k
Y = 4(1)(1) - 8(1) + 20
⇒ Y = 4 - 8 + 20
⇒ Y = -4 + 20
⇒ Y = 16
so, k = 16 (Y coordinate of vertex)
Now, substitute the value of a, k and h in .
⇒
Therefore, the vertex form of the given quadratic equation is
.
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Answer:
sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2
Step-by-step explanation:
The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.
There are many ways to make that pattern repeat with period π. one of them is this:
(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer
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The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.
