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1 year ago

What is the axis of symmetry of the graph of f(x)=−2x²+8x−2?

Mathematics

1 answer:

FromTheMoon [43]1 year ago

7 0

For the given parabola, the axis of symmetry is x = 2.

<h3>How to get the axis of symmetry?</h3>

For any given parabola, we define the axis of symmetry as a line that divides the parabola in two equal halves.

For a regular parabola, we define the axis of symmetry as:

x = h

Where h is the x-component of the vertex.

Remember that for the general parabola:

y = a*x^2 + b*x + c

The x-value of the vertex is:

h = -b/(2a)

Then for the function:

f(x)=−2x²+8x−2

We get:

h = -8/(2*-2) = 2

Then the axis of symmetry is x = 2.

If you want to learn more about parabolas, you can read:

brainly.com/question/1480401

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2 years ago

If sinA+cosecA=3 find the value of sin2A+cosec2A

Irina18 [472]

Answer:

$\sin 2A + \csc 2A = 2.122$

Step-by-step explanation:

Let $f(A) = \sin A + \csc A$ , we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:

$\csc A = \frac{1}{\sin A}$ (1)

$\sin^{2}A +\cos^{2}A = 1$ (2)

Now we perform the operations: $f(A) = 3$

$\sin A + \csc A = 3$

$\sin A + \frac{1}{\sin A} = 3$

$\sin ^{2}A + 1 = 3\cdot \sin A$

$\sin^{2}A -3\cdot \sin A +1 = 0$ (3)

By the quadratic formula, we find the following solutions:

$\sin A_{1} \approx 2.618$ and $\sin A_{2} \approx 0.382$

Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

$\sin A \approx 0.382$

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

$A \approx 22.457^{\circ}$

Then, the values of the cosine associated with that angle is:

$\cos A \approx 0.924$

Now, we have that $f(A) = \sin 2A +\csc2A$ , we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used: