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Dmitry_Shevchenko [17]
2 years ago
13

How do i reflect something on a grid?

Mathematics
1 answer:
Xelga [282]2 years ago
4 0

Answer:

Think of reflect as looking in a mirror. The question should tell you how your reflecting. It might say "reflect the rectangle over the y axis"  (Look at the attachment below to see example).

Step-by-step explanation:

I can help more if I see the question. But usually questions ask you to reflect over the y or x axis.

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Find all the zeros of the equation x^4-6x^2-7x-6=0 Explain please.
Alina [70]
<h3>Answer:</h3>
  • zeros are {-2, 3, (-1±i√3)/2}
<h3>Step-by-step explanation:</h3>

I like to look at a graph of the function to see where the zeros might be. Here, there are x-intercepts at x=-2 and x=3. These can be factored out using synthetic division to find the factorization to be ...

... (x +2)(x -3)(x² +x +1) = 0

By completing the square, using the quadratic formula, or by looking at the graph of it, the complex roots of the quadratic factor can be found to be ...

... x = (-1 ±i√3)/2

_____

The second attachment shows my synthetic division. The first division takes out the root x=3 to give a quotient of x³ +3x² +3x +2. The second division takes out the root -2 to give the quotient of x² +x +1. (You can see that I tried -1 as a root first.)

The graph shows both the quartic and the quadratic factor of it. The latter has a leading coefficient of 1 and a vertex at (-1/2, 3/4), so you know the complex roots are -1/2 ±i√(3/4).

_____

<em>From the beginning</em>

There is only a very complicated formula for the roots of a quartic equation, so these are usually solved by machine or by some form of trial and error (iteration). There are some helps, like Descarte's Rule of Signs, and the Rational Root theorem.

Here, the former looks at the one sign change in the coefficients to tell you there will be 1 positive real root. Changing the sign of the odd-degree terms makes there be 3 sign changes, so there will be 3 or 1 negative real roots. Thus, we're assured at least two real roots, one of each sign.

We can look at the constant term to find the y-intercept to be -6. We can add the coefficients to find the value of the function is -18 for x=1, so the positive real root is larger than 1.

The Rational Root theorem says any rational roots will be factors of 6, the constant term. Choices are 1, 2, 3, 6. We have already eliminated 1 as a possibility, and we consider it unlikely that 6 will be a root. (The 4th power overwhelms the other terms in the function.) We tried 2 and found it doesn't work (this was before we graphed the function). The attached division result shows that 3 is a root, as does the graph.

Once you get down to a quadratic, you can find the remaining roots in the usual way. Because it is so simple to read them from the graph, we decided to graph the quadratic factor.

_____

<em>Comment on terminology</em>

"root" and "zero" are essentially the same thing when the function is equated to zero, as here. The terms refer to the value(s) of x that make the polynomial function evaluate to zero.

8 0
3 years ago
The parent function f(x) = x3 and its translation, g(x), are shown on the graph.
NNADVOKAT [17]

The resulting function g(x) = (x-5)^3 + 3 shows a horizontal translation to the right by 5 units and vertical translation up by 3 units

<h3>Translation of functions</h3>

Quadratic functions are functions that has a leading degree of 2.

Given the parent function as shown:

f(x) = x^3

The resulting function g(x) = (x-5)^3 + 3 shows a horizontal translation to the right by 5 units and vertical translation up by 3 units

Learn more on translation here; brainly.com/question/12861087

#SPJ1

5 0
2 years ago
4xy + y = w<br><br> solve for y<br><br> pls show work
Soloha48 [4]

Answer:

y = w/4x+1

Step-by-step explanation:

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How many inches in a full step?
UNO [17]

Answer:

according to google there are 30 inches in a full step

Step-by-step explanation:

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