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tamaranim1 [39]
3 years ago
12

What is the vertex of the absolute value function defined by ƒ(x) = |x + 2| + 4?

Mathematics
2 answers:
Marrrta [24]3 years ago
4 0

Answer:

C. (-2,4)

Step-by-step explanation:

We have been given a function f(x)=|x+2|+4 and we are asked to find the vertex of our absolute value function.

The rules for the translation of a function are as follows:  

f|x-h|=\text{Graph shifted to right by h units}

f|x+h|=\text{ Graph shifted to left by h units}

f|x|+h=\text{ Graph shifted upward by h units}

f|x|-h=\text{ Graph shifted down by h units}

Upon comparing our absolute function with above transformations we can see that our function is shifted to two units right of the origin(0,0) so x coordinate of our absolute function will be -2.

Our function is shifted upward from origin by 4 units, therefore, y-coordinate of our absolute value function will be 4.

f(x)=|x--2|+4

Therefore, the vertex of our absolute value function will be on point (-2,4) and option C is the correct choice.

defon3 years ago
4 0

Answer: C. (-2,4)

Step-by-step explanation:

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\textsf{12.} \quad y = 6x - 5

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Step-by-step explanation:

<h3><u>Question 12</u></h3>

Find the slope of the line by substituting two points from the given table into the slope formula.

<u>Define the points</u>:

  • Let (x₁, y₁) = (2, 7)
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\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6

Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:

\implies y-y_1=m(x-x_1)

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<h3><u>Question 17</u></h3>

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Therefore, two points on the line are:

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The y-intercept is the y-value when x = 0.

Therefore, the y-intercept of the line is -2.

\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}

Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for <em>m</em> to find the slope:

\implies y=mx+b

\implies -3=m(4)-2

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\implies m=-\dfrac{1}{4}

Therefore, the equation of the line is:

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