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3 years ago

Describe the transformation from the graph of f(x) =ax^2 to the graph of g(x) = a(x-h)^2+k

Mathematics

1 answer:

MrRa [10]3 years ago

8 0

Answer: Step-by-step explanation:

f(x)=ax^2→g(x)=a(x-h)^2+k

The horizontal shift depends on the value of h. The horizontal shift is described as:

g(x)=f(x+h) - The graph is shifted to the left h units.

g(x)=f(x−h) - The graph is shifted to the right h units.

Hence, in the question above, Horizontal Shift: Right h Units

The vertical shift depends on the value of k. The vertical shift is described as:

g(x)=f(x)+k - The graph is shifted up k units.

g(x)=f(x)−k - The graph is shifted down k units.

Therefore, in the question above, Vertical Shift: Up k Units

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2 thirds of the product of 3 octavos and 16

Mazyrski [523]

Answer:4

Step-by-step explanation:

finding the product of 2 numbers means that you have to multiply those numbers

when multiplying fractions , numerators are multiplied by numerators and denominators by denominators

therefore product of 3/8 and 16 is 6

next we have to find 2/3 of 6

'of' operator means multiplication

answer is 4

hope it helps

mark brainliest

xoxo

6 0

3 years ago

Steve and Ben have some money in their wallets. If Steve gives Ben $3, Ben will have twice as much as Steve. If Ben gives Steve

Zigmanuir [339]

Answer:

Money owned by Steve = $11

Money owned by Ben = $13

Step-by-step explanation:

Let x denotes the money owned by Steve and y denotes the money owned by Ben.

Then, Steve gives $3 to Ben

Money left with Steve = x-3 and Ben = y+3

Now, Ben will have twice as much as Steve.

⇒ y+3 = 2(x-3) .............(1)

If Ben gives Steve $7

Money left with Steve = x+7 and Ben = y-7

Then, the amount Ben has will be one-third that of Steve’s.

⇒ y-7 = $\frac{1}{3}$ (x+7) ..........(2)

Solving equation (1) and (2) by elimination method, we get

x = 11 and y = 13

⇒ Money owned by Steve = $11

Money owned by Ben = $13

5 0

3 years ago

What is the exact circumference of a circle with a diameter of 40 feet?

Irina-Kira [14]

Answer:

The answer is

Step-by-step explanation:

Circumference of a circle is πd

Where d is the diameter

From the question

d = 40 feet

Circumference of the circle is

40π

= 125.66

= 126 feet to the nearest whole number

Hope this helps you

7 0

3 years ago

Find the midpoint of AB for: A(7,0)|and B(0,3)

liberstina [14]

Answer:

$\boxed {\boxed {\sf (\frac {7}{2}, \frac{3}{2}) \ or \ (3,5, 1.5) }}$

Step-by-step explanation:

The midpoint is essentially a point with the average of the 2 x-coordinates and the 2 y-coordinates.

The formula is:

$(\frac {x_1+x_2}{2}, \frac{y_1+y_2}{2})$

We are given two points: A (7,0) and B (0, 3). Remember points are written as (x, y).

Therefore,

$x_1= 7 \\y_1=0 \\x_2=0 \\x_2=3$

Substitute the values into the formula.

$(\frac {7+0}{2}, \frac{0+3}{2})$

Solve the numerators first.

$(\frac {7}{2}, \frac{3}{2})$

The midpoint can be left like this because the fractions are reduced, but it can be written as decimals too.

$(3.5, 1.5)$

3 0

3 years ago

BRAINLIESTTT ASAP! PLEASE HELP ME :)

GrogVix [38]

Answer:

1. Type of function: absolute value function

2. The three transformations from the parent function f(x) = |x| are:

Translation 3 units to the left
Vertical stretch with a scale factor of 2
Translation 5 units downward

Explanation:

1. Type of function

The parent function |x| is the absolute value function. It returns the positive value of the argument (x).

Thus the function f(x) = 2|x + 3| - 5 is also an absolute value function.

It returns the positive value of x + 3, then multiplyes it by 2, and finally subtract 5.

This is a piecewise function.

For the values of x ≥ - 3, the output is 2(x +3) - 5 = 2x + 6 - 5 = 2x + 1.

For the values of x < - 3, the output is 2 (-x - 3) - 5 = -2x - 6 - 5 = -2x - 11.

The vertex of this function is at x = - 3: 2 (- 3 + 3) - 5 = 2(0) - 5 = 0 - 5 = 5.

Thus the vertex is (-3, 5).

2. Transformations from the parent function f(x) = |x|.

When you know the parent function and the daughter function you can know the transformations done of the former to get the later by some simple rules.

a) Translation in the horizontal direction.

When you add a positive value to the argument the function is translated to the left.

Thus, when you add 3 to x, |x| becomes |x + 3| and it is a translation 3 units to the left.

b) Vertical stretch

When you multiply the argument by a constant, the function stretches vertically.

Thus, when you multiply |x + 3| by 2, to get 2|x + 3|, the function is vertically stretched by a scale factor of 2.

c) Vertical translation

When you subtract a constant value from the function, you translate it downward.

Thus, when you subtract 5 from 2|x + 3| - 5, you translate the function 5 units downward.

6 0

3 years ago