Mathematics: What is the parent function translated 3 units down in vertex form

What is the parent function translated 3 units, №13244676, 11.09.2020 19:28

Mathematics

Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformation of the given function? y=|6x-2|-7 (1/3,7); x=1/3; translated to the right 1/3 unit and up 7 units (1/3,7); x=1/3; translated to the left 1/3 unit and down 7 units (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units (1/3,-7); x=1/3; translated to the left 1/3 unit and up 7 units

Step-by-step answer

P Answered by PhD

8

(1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units

Step-by-step explanation:

The parent function is:

g(x) = IxI

And we have:

f(x) = I6x - 2I - 7

We canr rewrite f to get:

f(x) = 6*Ix - 1/3I - 7

Then, now let's define some transformations:

If we start with g(x), a translation of N units to the right is:

f(x) = g(x - N)

if we start with g(x), a translation of N units up is:

f(x) = g(x) + N

A translation down would be:

f(x) = g(x) - N

And a vertical dilation of scale factor A is written as:

f(x) = A*g(x)

Then in this case we have:

A translation to the right of 1/3 units.

A dilation of scale factor 6.

A translation down of 7 units.

And the axis of symmetry will be when the absolute value part is equal to zero, or when

6*Ix - 1/3I = 0

And that is when x = 1/3.

Then the correct option is:

(1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units

Mathematics

Compare the function with the parent function. Without graphing, what are the vertex, axis of symmetry, and transformation of the given function? y=|6x-2|-7 (1/3,7); x=1/3; translated to the right 1/3 unit and up 7 units (1/3,7); x=1/3; translated to the left 1/3 unit and down 7 units (1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units (1/3,-7); x=1/3; translated to the left 1/3 unit and up 7 units

Step-by-step answer

P Answered by PhD

8

(1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units

Step-by-step explanation:

The parent function is:

g(x) = IxI

And we have:

f(x) = I6x - 2I - 7

We canr rewrite f to get:

f(x) = 6*Ix - 1/3I - 7

Then, now let's define some transformations:

If we start with g(x), a translation of N units to the right is:

f(x) = g(x - N)

if we start with g(x), a translation of N units up is:

f(x) = g(x) + N

A translation down would be:

f(x) = g(x) - N

And a vertical dilation of scale factor A is written as:

f(x) = A*g(x)

Then in this case we have:

A translation to the right of 1/3 units.

A dilation of scale factor 6.

A translation down of 7 units.

And the axis of symmetry will be when the absolute value part is equal to zero, or when

6*Ix - 1/3I = 0

And that is when x = 1/3.

Then the correct option is:

(1/3,-7); x=1/3; translated to the right 1/3 unit and down 7 units

Mathematics

The transformations to the parent function of a quadractic equation are given below. Write an equation of the new function in vertex form. Solve Translated 3 units down

Step-by-step answer

P Answered by PhD

f(x) = x^2 -3

Step-by-step explanation:

A function is translated down 3 units by subtracting 3 from the function value. For the parent function f(x) = x^2, the translated function is ...

f(x) = x^2 -3

Comment on vertex form

The full "vertex form" has the values of the vertex coordinates in the equation explicitly. For vertex (h, k), the form is ...

f(x) = a(x -h)^2 +k

We have moved the vertex from (0, 0) to (0, -3). The vertical scale factor (a) remains 1. So, we could write the equation as ...

f(x) = 1(x -0)^2 -3 . . . . vertex form with unnecessary parts shown

Removing the identity elements doesn't change anything (though it requires a little practice to see them when they aren't there). So, with minor simplification, this becomes ...

f(x) = x^2 -3

Mathematics

Quadratic transformations c11t7 1. write the vertex form of a quadratic equation. 2. name the 3 ways that a parabola changes with different types of a values. 3. what does changing the h variable do to the graph of a quadratic? if h is positive how does the parabola move? if “h” is negative? 4. what does changing the k variable do to the graph of a quadratic? if k is positive how does the parabola move? if “k” is negative? 5. use the description to write the quadratic function in vertex form: the parent function f(x) = x2 is reflected across the

Step-by-step answer

P Answered by PhD

10

1. The vertex form of a quadratic equation is f(x) = a(x - h)² + k where (h, k) is the parabola formed by the equation. 2. The value of a affects the shape of the parabola. Three concrete ways showing this are: i. When a is negative ( a < 0), then the parabola opens downward ii. When a is positive ( a > 0), the the parabola opens upward ii. Lastly, when a reduces, the parabola shrinks. And when a increases, the parabola expands as well. 3. Since h directly affects the value of x, then it means that when h is increased by one unit, the parabola moves to the left by one unit. Similarly, if h decreases by 1 unit, it shifts to the right by one unit. Some textbooks call this as the parabola's horizontal shift. 4. The value of k directly affects the movement of the parabola across the y-axis. That means, if k is increased, the parabola goes up. And when k decreases, the graph goes down as well. 5. We have f(x) = 1(x)² as the original function with (h, k) = (0, 0). If we reflect it, across the x-axis, that means we negate the value across. So, we now have a new function, g(x), g(x) = -(x)². Based from the discussion regarding translations, if we move f(x) 5 units to the left, that means we are to increase the value of h by 5. So now, g(x) becomes g(x) = -(x - 5)² Applying the same concept, if we shift the graph 1 unit below, we decrease the value of k by 1. So we now have a final function of g(x) = -(x - 5)² - 1 6. Using the same initial function with 5, we have f(x) = 1(x)² with (h, k) = (0, 0). Now, since f(x) is to be compressed by 3, g(x) becomes g(x) = 1/3(x)² Translating 4 units to the right means decreasing the value of h by 4 and translating 2 units upwards means increasing the value of k by 2. Thus, we have g(x) = 1/3[x - (-4)]² + 2 Simplifying this, we'll have the new function as g(x) = 1/3(x + 4)² + 2

Mathematics

Quadratic transformations c11t7 1. write the vertex form of a quadratic equation. 2. name the 3 ways that a parabola changes with different types of a values. 3. what does changing the h variable do to the graph of a quadratic? if h is positive how does the parabola move? if “h” is negative? 4. what does changing the k variable do to the graph of a quadratic? if k is positive how does the parabola move? if “k” is negative? 5. use the description to write the quadratic function in vertex form: the parent function f(x) = x2 is reflected across the

Step-by-step answer

P Answered by PhD

10

1. The vertex form of a quadratic equation is f(x) = a(x - h)² + k where (h, k) is the parabola formed by the equation. 2. The value of a affects the shape of the parabola. Three concrete ways showing this are: i. When a is negative ( a < 0), then the parabola opens downward ii. When a is positive ( a > 0), the the parabola opens upward ii. Lastly, when a reduces, the parabola shrinks. And when a increases, the parabola expands as well. 3. Since h directly affects the value of x, then it means that when h is increased by one unit, the parabola moves to the left by one unit. Similarly, if h decreases by 1 unit, it shifts to the right by one unit. Some textbooks call this as the parabola's horizontal shift. 4. The value of k directly affects the movement of the parabola across the y-axis. That means, if k is increased, the parabola goes up. And when k decreases, the graph goes down as well. 5. We have f(x) = 1(x)² as the original function with (h, k) = (0, 0). If we reflect it, across the x-axis, that means we negate the value across. So, we now have a new function, g(x), g(x) = -(x)². Based from the discussion regarding translations, if we move f(x) 5 units to the left, that means we are to increase the value of h by 5. So now, g(x) becomes g(x) = -(x - 5)² Applying the same concept, if we shift the graph 1 unit below, we decrease the value of k by 1. So we now have a final function of g(x) = -(x - 5)² - 1 6. Using the same initial function with 5, we have f(x) = 1(x)² with (h, k) = (0, 0). Now, since f(x) is to be compressed by 3, g(x) becomes g(x) = 1/3(x)² Translating 4 units to the right means decreasing the value of h by 4 and translating 2 units upwards means increasing the value of k by 2. Thus, we have g(x) = 1/3[x - (-4)]² + 2 Simplifying this, we'll have the new function as g(x) = 1/3(x + 4)² + 2

Mathematics

The parent function f(x) = x2 is vertically compressed by a factor of 1/2 and translated 1 unit right and 3 units down to create g. identify g in vertex form.

Step-by-step answer

P Answered by Master

7

Since the function f(x)=x^2 is vertically compressed by a factor of 0.5 then the function is transformed in $f_1(x)=\frac{1}{2}x^2$

Now, f_1(x) is translated 1 unit right, obtaining the function $f_2(x)=\frac{1}{2}(x-1)^2$

Then, f_2(x) is translated 3 units down, obtaining the function

$g(x)=\frac{1}{2}(x-1)^2-3$ that is in vertex form and the vertex of g(x) is the point (1,-3)

Mathematics

The parent function f(x) = x2 is vertically compressed by a factor of 1/2 and translated 1 unit right and 3 units down to create g. identify g in vertex form.

Step-by-step answer

P Answered by Master

7

Since the function f(x)=x^2 is vertically compressed by a factor of 0.5 then the function is transformed in $f_1(x)=\frac{1}{2}x^2$

Now, f_1(x) is translated 1 unit right, obtaining the function $f_2(x)=\frac{1}{2}(x-1)^2$

Then, f_2(x) is translated 3 units down, obtaining the function

$g(x)=\frac{1}{2}(x-1)^2-3$ that is in vertex form and the vertex of g(x) is the point (1,-3)

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

What is the parent function translated 3 units down in vertex form

Faq

Try asking the Studen AI a question.