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3 years ago

How to graph y=|x-4| -3

Mathematics

1 answer:

Dafna11 [192]3 years ago

6 0

Okay, let's first establish some ground rules.

1) Whenever something is subtracted or added to x directly, it is a horizontal transformation. In other words, the function is shifted either left or right. Subtraction is right, addition is left.

EX: In y = (x - 4)^2, the function x^2 is moved 4 units to the right.

2) Whenever something is subtracted or added to the whole function, it is a vertical transformation. In other words, the function is shifted either up or down. Subtraction is down, addition is up.

EX: In y = x^2 + 4, the function x^2 is moved 4 units up.

Here, the function |x| is moved 4 units to the right and 3 units down. So, the vertex will be at point (4, -3). Being more technical:

m = -1 if -∞ < x ≤ 4 and m = 1 if 4 < x < ∞

Hope this helps, let me know if I messed up!

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rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The w

Mice21 [21]

S=2(4x+2x)+4x^2=4x^2+12x

4x^2+12x=7
4x^2+12x-7=0
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3 years ago

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musickatia [10]

Answer:

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3 years ago

Write the equation in slope-intercept form then change it to standard form with integer coefficients.

SCORPION-xisa [38]

Answer:

1. Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

2. Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

3. Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

Step-by-step explanation:

Slope intercept form: $y = mx + b$

where:

$y$ = y-coordinate
$m$ = slope
$x$ = x-coordinate
$b$ = y-intercept

Standard form: $Ax + By = C$

$\textsf{1. as} \ m=2: \ \ y = 2x + b$

$\textsf{at} \ (6, 8): \ \ 8 = 2(6) + b$

$\implies b = -4$

Slope-intercept form: $y = 2x - 4$

Standard form: $2x - y = 4$

$\textsf{2. as} \ \ m = \dfrac12: \ \ y = \dfrac12x + b$

$\textsf{at} \ (4, 1): \ \ 1 = \dfrac12(4) + b$

$\implies b = -1$

Slope-intercept form: $y = \dfrac12x - 1$

Standard form: $x - 2y = 2$

$\textsf{3. as} \ \ m = \dfrac45: \ \ y = \dfrac45x + b$

$\textsf{at} \ (1,5): \ \ 5 = \dfrac45(1) + b$

$\implies b = \dfrac{21}{5}$

Slope-intercept form: $y = \dfrac45x + \dfrac{21}{5}$

Standard form: $4x -5y = - 21$

7 0

2 years ago

Find the solutions to x2 = 24. O A. x = +216 O B. x = 16.6 O C. x= 46 O D. x = +62

babymother [125]

Answer:

x =±2 sqrt(6)

Step-by-step explanation:

x^2 = 24

Take the square root of each side

sqrt(x^2) = sqrt(24)

x = ±sqrt(4*6)

x =±sqrt(4) sqrt(6)

x =±2 sqrt(6)

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3 years ago

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bonufazy [111]

The answer is false :)

8 0

3 years ago