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Brums [2.3K]
3 years ago
11

What is the purpose of "completing the square"?

Mathematics
1 answer:
zysi [14]3 years ago
8 0

Step-by-step explanation:

When you complete the square, you change the equation so that the left side of the equation is a perfect square trinomial. But mainly completing the square is a technique that transforms your quadratic equation from an equation that can't be factored into one that can.

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The charges for a delivery service are explained in the table what is the rate of change
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3 years ago
Please help with the attached question. Thanks
Mademuasel [1]

Answer:

Choice A) F(x) = 3\sqrt{x + 1}.

Step-by-step explanation:

What are the changes that would bring G(x) to F(x)?

  • Translate G(x) to the left by 1 unit, and
  • Stretch G(x) vertically (by a factor greater than 1.)

G(x) = \sqrt{x}. The choices of F(x) listed here are related to G(x):

  • Choice A) F(x) = 3\;G(x+1);
  • Choice B) F(x) = 3\;G(x-1);
  • Choice C) F(x) = -3\;G(x+1);
  • Choice D) F(x) = -3\;G(x-1).

The expression in the braces (for example x as in G(x)) is the independent variable.

To shift a function on a cartesian plane to the left by a units, add a to its independent variable. Think about how (x-a), which is to the left of x, will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by a units, subtract a from its independent variable.

For example, G(x+1) is 1 unit to the left of G(x). Conversely, G(x-1) is 1 unit to the right of G(x). The new function is to the left of G(x). Meaning that F(x) should should add 1 to (rather than subtract 1 from) the independent variable of G(x). That rules out choice B) and D).

  • Multiplying a function by a number that is greater than one will stretch its graph vertically.
  • Multiplying a function by a number that is between zero and one will compress its graph vertically.
  • Multiplying a function by a number that is between -1 and zero will flip its graph about the x-axis. Doing so will also compress the graph vertically.
  • Multiplying a function by a number that is less than -1 will flip its graph about the x-axis. Doing so will also stretch the graph vertically.

The graph of G(x) is stretched vertically. However, similarly to the graph of this graph G(x), the graph of F(x) increases as x increases. In other words, the graph of G(x) isn't flipped about the x-axis. G(x) should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points (x, y)'s that are on the graph of F(x) fit into the expression y = F(x) = 3\sqrt{x - 1}.

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3 years ago
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My mystery number has 5 tens and 29 ones?
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In the Treasure, Treasure! video game, players gain and lose points by finding and losing treasure. In Level 2, Leslie earned
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Answer:

. finding and losing treasure. In level 2, Leslie earned -22 points when a storm blew a treasure chest off her ship. Then, she earned 34 ... a storm blew a treasure chest off her ship. Then, she earned 34 points for finding more treasure on the deserted island. What is the overall change in Leslie's score during level 2? ansver.

Step-by-step explanation:

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Help 10 POINTS MATH IS NOT MY STRONG SUIT
Masja [62]

Answer:

infinite number of solutions

Step-by-step explanation:

Work with the second equation.  Subtract 8x from both sides.

- 4y + 8x - 8x = -8x - 12                   Collect like terms.

-4y = - 8x - 12                                   Divide by - 4

-4y/-4 = - 8x/-4 - 12/-4

y = 2x + 3

That is exactly the same line as the first given.  There is an infinite number of solutions.

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3 years ago
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