Can someone please help!!!

If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating 11 units to the left:

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating 5 units down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

Translating 8 units to the right:

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating 1 unit down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1

7 0

3 years ago

What is growth mindset? Describe growth mindset.

Nastasia [14]

Answer:

Growth Mindset: “In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment,” Dweck wrote.

Step-by-step explanation:

8 0

3 years ago

Bob and Sue enter a race. Bob runs an average of 12 kilometers per hour, and Sue runs an average of 8 kilometers per hour. If Bo

solniwko [45]

Bob = 12 x T
Sue= 8 (T +2)

12T = 8T + 16
12T-8T=8T-8T +16
4T = 16
4T/4 = 16/4
T= 4 HOURS

PLUG T BACK INTO
12(4) = 8(4) + 16
48=48

DISTANCE = 48 kilometers

5 0

3 years ago

Read 2 more answers

A bill for Rs 3235 was drawn on Feb. 3, 1998 at 6 months and discounted on March 3, 1998 at 8 % p.a. Find the value of the bill

Fantom [35]

Answer:

RS 3127.166

RS 107.834

Step-by-step explanation:

6 month bill :

Drawn date = Feb, 3

Discounted date = March 3,

Difference = 1 month

6 month - 1 month = 5 months = 5 * 30 = 150 days

Value of the bill :

P(1 - rate * time)

3235(1 - 0.08 * 150/360)

3235(1 - 0.08 * 0.4166666)

3235(1 - 0.0333333)

3235(0.9666666)

= Rs3127.1666

Value of bill = 3127.166

Bankers gain = 3235 - 3127.166 = 107.834

6 0

3 years ago

Heather has a bag with 16 red blocks, 11 blue blocks, 9 purple blocks, 15 green blocks, 8 yellow blocks, and 20 orange blocks. I

forsale [732]

There is a total of 16+11+9+15+8+20 = 79 blocks. Since she is replacing the block each time it is drawn, the probability that she draws an orange block is always the same (10 draws or 500 draws). Since 20 of the blocks are orange, the probability would be

20/79 or

D) 0.25

3 0

3 years ago