F(x)=-x^2 -4x -2, for this equation find the solutions, the coordinates of the vertex, and the axis of the symmetry.
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Answer:
4.4
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
where:
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The <u>period</u> is the horizontal distance between consecutive peaks, which is the same as <u>twice the horizontal distance between the intersection of the curve and the mid-line</u>.
Given consecutive points of intersection between the curve and the mid-line:
- (3.7, 5)
- (5.9, 5)
Therefore, the horizontal distance between these two points is:
5.9 - 3.7 = 2.2
⇒ Period = 2.2 × 2 = 4.4
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To create the equation for the function.
From inspection of the given graph:
- Amplitude (A) = 6
- Mid-line is y = 5
- Vertical shift (D) = +5
Period = 2π/B = 4.4 ⇒ B = 5π/11
Phase Shift (C) = -3.7
Substituting the values into the standard form:
