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stealth61 [152]
2 years ago
12

Convert the following quadratics from standard form to vetex form, then graph them.

Mathematics
1 answer:
9966 [12]2 years ago
4 0

1. Answer:  y = (x + 3)² - 4

<u>Step-by-step explanation:</u>

Vertex format is: y = a(x - h)² + k

y = x² + 6x + 5

y - 5 = x² + 6x       <em>subtracted 5 from both sides</em>

y - 5 + \bigg(\dfrac{6}{2}\bigg)^2 = x² + 6x + \bigg(\dfrac{6}{2}\bigg)^2    <em>completed the square</em>

y + 4 = (x + 3)²        <em>simplified</em>

y = (x + 3)² - 4        <em>subtracted 4 from both sides</em>

Equation is now in vertex form!

To graph the equation, plot the following points:

  • vertex (h, k) = (-3, -4)
  • y-intercept from the original equation (0, c) = (0, 5)
  • mirror image of y-intercept (-6, 5)

2. Answer:  y = -(x + 3)² + 2

<u>Step-by-step explanation:</u>

Vertex format is: y = a(x - h)² + k

y = -x² - 6x - 7

y + 7 = -x² - 6x       <em>added 7 to both sides</em>

-y - 7 = x² + 6x         <em>divided both sides by -1</em>

-y - 7 + \bigg(\dfrac{6}{2}\bigg)^2 = x² - 6x + \bigg(\dfrac{6}{2}\bigg)^2    <em>completed the square</em>

-y + 2 = (x + 3)²        <em>simplified</em>

y - 2 = -(x + 3)²        <em>divided both sides by -1</em>

y = -(x + 3)² + 2        <em>subtracted 4 from both sides</em>

Equation is now in vertex form!

To graph the equation, plot the following points:

  • vertex (h, k) = (-3, 2)
  • y-intercept from the original equation (0, c) = (0, -7)
  • mirror image of y-intercept (-6, -7)

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Answer:

a.\ m=2,\ \text{the line is rising}\\\\b.\ m=-\dfrac{5}{4},\ \text{the line is falling}\\\\c.\ m=0,\ \text{the line is horizontal}\\\\d.\ m\ is\ unde fined,\ \text{the line is vertical}

Step-by-step explanation:

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

If

m > 0, then a line is rising

m < 0, then a line is falling

m = 0, then a line is horizontal

m is undefined, then a line is vertical

<h2>a.</h2>

(2, 1) and (4, 5)

m=\dfrac{5-1}{4-2}=\dfrac{4}{2}=2>0\to\text{rising}

<h2>b.</h2>

(-1, 0) and (3, -5)

m=\dfrac{-5-0}{3-(-1)}=\dfrac{-5}{4}=-\dfrac{5}{4}

<h2>c.</h2>

(2, 1) and (-3, 1)

m=\dfrac{1-1}{-3-2}=\dfrac{0}{-5}=0\to\text{horizontal}

<h2>d.</h2>

(-1, 2) and (-1, -5)

m=\dfrac{-5-2}{-1-(-1))}=\dfrac{-7}{0}\ \text{UNDEFINED}\to\text{vertical}

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3 years ago
Say that Thailand has a workforce of 35,709,487 people, each of whom earns an average salary of (equivalent USD) $8,630 annually
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The income tax rate must be 29%.

Given that,

Thailand has a workforce of 35,709,487 people, each of whom earns an average salary of (equivalent USD) $8,630 annually.

If the Thai government wants to raise $70 billion in tax revenue,

We have to find,

The approximately where should it set the income tax rate?

According to the question,

Thailand has a workforce of 35,709,487 people, each of whom earns an average salary of (equivalent USD) $8,630 annually.

\rm Total \ income = Number \ of \ people \times Income \ per \ person\\\\Total \ income = 35,709,487 \times 8,630\\\\Total \ income = 308,172,872,810

If the Thai government wants to raise $70 billion in tax revenue,

Then,

The income tax rate is,

\rm Tax\  rate = \dfrac{70,000,000,000,}{308,172,872,810}\\\\Tax \ rate = 0.29\\\\Tax \ rate = 29 \ percent

Hence, The income tax rate must be 29%.

For more details refer to the link given below.

brainly.com/question/16016455

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Simplify y-2/3/y+1/5
liberstina [14]

Answer:

\frac{15y-10}{15y-3}

Step-by-step explanation:

First at all, we need to use a=\frac{a}{1} to convert this expression into a fraction, like:

y-\frac{2}{3} to convert into \frac{y}{1} -\frac{2}{3}.

Expand the fraction to get the least common denominator, like

\frac{3y}{3*1}-\frac{2}{3}

Write all numerators above the common denominator, like this:

\frac{3y-2}{3}

The bottom one used the same way to became simplest form, like this:

y+\frac{1}{5}

\frac{y}{1} +\frac{1}{5}

\frac{5y}{5*1}+\frac{1}{5}

\frac{5y+1}{5}

And it became like this:

\frac{3y-2}{3}/\frac{5y+1}{5}

Now, we are going to simplify this complex fraction. We can use cross- multiply method to simplify this fraction.

\frac{3y-2}{3}*\frac{5y+1}{5}

3y-2(5) and 5y-1(3)

and it will becomes like this in function form:

\frac{3y-2(5)}{5y+1(3)}

Then, we should distribute 5 through the parenthesis

\frac{15y-10}{5y+1(3)}

\frac{15y-10}{15y+3}

And.... Here we go. That is the answer.

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3 years ago
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