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7 months ago

Re-write the quadratic function below in Standard Form y=-5(x+1)²+7

Mathematics

2 answers:

Arturiano [62]7 months ago

7 0

Answer:

y = - 5x² - 10x + 2

Step-by-step explanation:

y = - 5(x + 1)² + 7 ← expand (x + 1)² using FOIL

= - 5(x² + 2x + 1) + 7 ← distribute parenthesis by - 5

= - 5x² - 10x - 5 + 7 ← collect like terms

= -5x² - 10x + 2 ← in standard form

julsineya [31]7 months ago

3 0

Answer: y = -5x² - 10x + 2

Step-by-step explanation:

Given quadratic function

y = -5 (x + 1)² + 7

Given requirement

Quadratic Standard Form: y = ax² + bx + c

Simplify the exponents

y = -5 (x + 1) (x + 1) + 7

y = -5 (x² + x + x + 1) + 7

y = -5 (x² + 2x + 1) + 7

Expand the parenthesis by distributive property

y = (-5) · x² + (-5) · 2x + (-5) · 1 + 7

y = -5x² + (-10x) + (-5) + 7

y = -5x² - 10x - 5 + 7

Combine like terms

$\Large\boxed{y=-5x^2-10x+2}$

Hope this helps!! :)

Please let me know if you have any questions

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Calculate the value of the sample variance. Round your answer to one decimal place. 9_5,9_5,2,9_5

Ugo [173]

Answer:

$s^2 = 0.01$

Step-by-step explanation:

Given

Values: 9/5, 9/5, 2, 9/5

Required

Calculate the sample variance

Sample variance is calculated using:

$s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}$

First, we calculate the mean

$\overline x = \frac{\sum x}{n}$

$\overline x = \frac{9/5 + 9/5 + 2 + 9/5}{4}$

$\overline x = \frac{7.4}{4}$

$\overline x = 1.85$

$s^2 = \frac{\sum (x_i - \overline x)^2}{n - 1}$ becomes

$s^2 = \frac{(9/5 - 1.85)^2+(9/5 - 1.85)^2+(2 - 1.85)^2+(9/5 - 1.85)^2}{4 - 1}$

$s^2 = \frac{(-0.05)^2+(-0.05)^2+(0.15)^2+(-0.05)^2}{4 - 1}$

$s^2 = \frac{0.0025+0.0025+0.0225+0.0025}{3}$

$s^2 = \frac{0.03}{3}$

$s^2 = 0.01$

Hence, the variance is 0.01

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2 years ago

For the given table of values for a polynomial function, where must the zeros of the function lie?

Jet001 [13]

Answer:

A. Between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

The zeroes of a function occur whenever a value of x returns zero. To predict where the zeroes lie, determine the interval(s) where the function crosses the x-axis. This occurs when either $f(x)$ goes from a negative value to a positive value or vice versa.

From $x=3.0$ and $x=3.5$ , the y-values go from 4.0 (positive) to -0.2 (negative), respectively. Therefore, there must be a zero in this interval.

From $x=4.0$ and $x=4.5$ , the y-values go from -0.8 (negative) to 0.1 (positive), respectively. Therefore, there must also be a zero in this interval.

Thus, the zeros of this function occur between 3.0 and 3.5 and between 4.0 and 4.5, leading to answer choice A.

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IceJOKER [234]

7x-x=19-7
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