Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) =
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = () + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases
Given:
The graph of a function .
To find:
The interval where .
Solution:
From the given graph graph it is clear that, the function before x=0 and after x=3.6 lies above the x-axis. So, for
and
.
The function between x=0 and x=3.6 lies below the x-axis. So, for
.
Now,
For , the graph of h(x) is above the x-axis. So,
.
For , the graph of h(x) is below the x-axis. So,
.
For , the graph of h(x) is below the x-axis. So,
.
Only for the interval , we get
.
Therefore, the correct option is A.
The double angle formula for the sine is
The right hand side is exactly your expression, where
So, rewriting the expression from right to left, we have
