<h3>Axis of symmetry is 0 and vertex is (0, -1)</h3>
<em><u>Solution:</u></em>
<em><u>Given is:</u></em>
We have to find the vertex and axis of symmetry
<em><u>The general equation is given as:</u></em>
Comparing with given equation,
a = 2
b = 0
c = -1
<em><u>The axis of symmetry is given as:</u></em>
Thus axis of symmetry is 0
The x coordinate of the vertex is the same
x coordinate of the vertex = 0
h = 0
The y coordinate of the vertex is:
k = f(h)
k = f(0)
Thus, y coordinate of the vertex is -1
Therefore, vertex is (0, -1)
Answer:
Step-by-step explanation:
Answer:
6. was Narbada alienated ...?
7. did Pratima make ...?
8. did Zayasha wander ...?
9. Did Sachin behave as if...?
10. did susan look ...?
12. do <u>sarina and sazina</u> jump ...? (plural noun)
13. Were ... and ... aghast to...?
Step-by-step explanation:
yes/ no question:
Past simple: Did + S + V-bare...?
Passive voice (Past simple): Was/ Were + S + V3/ed (<em>past participle</em>)
Answer:
- increasing: (π/2, 3π/2)
- decreasing: [0, π/2) ∪ (3π/2, 2π]
- minimum: -16 at x=π/2
- maximum: 16 at x=3π/2
Step-by-step explanation:
If all you want are answers to the questions, a graphing calculator can provide them quickly and easily. (see attached)
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If you need an algebraic solution, you need to find the zeros of the derivative.
f'(x) = -16cos(x)sin(x) -16cos(x) = -16cos(x)(sin(x) +1)
The product is zero where the factors are zero, at x=π/2 and x=3π/2.
These are the turning points, where the function changes from decreasing to increasing and vice versa.
(sin(x)+1) is non-negative everywhere, so the sign of the derivative is the opposite of the sign of the cosine function. This tells us the function f(x) is increasing on the interval (π/2, 3π/2), and decreasing elsewhere (except where the derivative is zero).
The function local extrema will be where the derivative is zero, so at f(π/2) (minimum) and f(3π/2) (maximum). We already know that cos(x) is zero there, so the extremes match those of -16sin(x).
