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3 years ago

verbally explain how to obtain the graph of the quadratic function f(x)=-2(x+3)^2-4 from the graph of y=x^2.

Mathematics

1 answer:

Ksivusya [100]3 years ago

7 0

Answer:

The graph f(x)= $-2(x+3)^2-4$ is a reflection over the x-axis, vertical stretch by a factor of 2, a horizontal translation left 3 units and a vertical translation 4 units down of the graph y= $x^2$ .

Step-by-step explanation:

The graph f(x) is reflected over the x-axis because the negative is outside of the parenthesis.

it's a vertical stretch by a factor of 2 because 2 is outside of the parenthesis and is greater than 1.

(x+3) is a horizontal translation left 3 units because it is inside the parenthesis.

-4 is vertical translation 4 units down because it is outside of the parenthesis.

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A circle has its center at (0,0) and passes through the point (0,9). What is the standard equation of the circle?

Alexxandr [17]

Answer:

x^2+y^2=9^2

Step-by-step explanation:

The standard equation of a circle is:

$(x-h)^2+(y-k)^2=r^2$

Where the center of a circle is (h,k) and r is the radius of the circle. In this case because a circle is equidistant from the center and we have a point where it passes through 9 that means that the radius is 9. However, since the standard equation states that we must write r in the form of $r^2$ this means that $r^2=9^2$ . Therefore by plugging in the values we have:

$(x-0)^2+(y-0)^2=9^2\\\\x^2+y^2=9^2$

7 0

2 years ago

Given the function f(x) = 2x+4 and the domain: {-1,0,1},determine the range

Svetlanka [38]

Answer:

f(x) = 2x + 4 domains {-1, 0, 1}

range {2, 4, 6}

(please mark brain if this helps and is correct)

Step-by-step explanation:

to solve f(x) to find the range you would want to input all the domain numbers in the equation f(x) to get the range of all the numbers you need

step 1: take the first domain number and input it into your equation where x is

ex: 2x + 4 [2(-1) + 4] = -2 + 4 = 2

step 2: add the second domain number and input it into your equation where x is

ex: 2x + 4 [2(0) + 4] = 0 + 4 = 4

step 3: add the last domain number and input it into your equation where x is

ex: 2x + 4 [2(1) + 4] = 2 + 4 = 6

Now we have determined what the range is

6 0

2 years ago

Which equation below would be perpendicular to the line y = 2?

nadya68 [22]

Answer:
A) y=1/5x
Step-by-step explanation:
Coz, the way you identify a perpendicular line is by looking for its negative reciprocal. The neagtive reciprocal of 5= 1/5
Now, to check the ans we can multiply the negative reciprocal by "m"
(m in y=mx+c or y=mx+b)
in this case the "m" is stated as 5, so all we need to do is 1/5*5 if the ans is 1 then your ans is right....and over here it is
So thats how you identify & check perpendicular lines!

3 0

2 years ago

Read 2 more answers

A fair coin is tossed three times and the events A, B, and C are defined as follows: A: \{ At least one head is observed \} B: \

Yanka [14]

Answer:

a) $P(A)=0.875$

b) $\text{P(A or B)}=0.875$

c) $\text{P((not A) or B or (not C))}=0.625$

Step-by-step explanation:

Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.

To find : The following probabilities by summing the probabilities of the appropriate sample points ?

Solution :

The sample space is

S={HHH,HHT,HTT,HTH,TTT,TTH,THH,THT}

n(S)=8

A: At least one head is observed

i.e. A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

n(A)=7

B: At least two heads are observed

i.e. B={HHH,HTT,TTH,THT}

n(B)=4

C: The number of heads observed is odd.

i.e. C={HHH,HTT,THT,TTH}

n(c)=4

a) Probability of A, P(A)

$P(A)=\frac{n(A)}{n(S)}$

$P(A)=\frac{7}{8}$

$P(A)=0.875$

b) P(A or B)

Using formula,

$\text{P(A or B)}=P(A)+P(B)-\text{P(A and B)}$

$\text{P(A or B)}=\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{\text{n(A and B)}}{n(S)}$

$\text{P(A or B)}=\frac{7}{8}+\frac{4}{8}-\frac{4}{8}$

$\text{P(A or B)}=\frac{7}{8}$

$\text{P(A or B)}=0.875$

(c) P((not A) or B or (not C))

A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

not A = {TTT} = 1

B={HHH,HTT,TTH,THT}

C={HHH,HTT,THT,TTH}

not C = {HHT,HTH,THH,TTT} = 4

So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5

$\text{P((not A) or B or (not C))}=\frac{5}{8}$

$\text{P((not A) or B or (not C))}=0.625$

4 0

2 years ago

Determine the value for x in the picture below.<br> Please help me

Alex787 [66]

Given:

The figure of a right angle triangle.

A line segment intersect the two sides and parallel to third side of the triangle

To find:

The value of x.

Solution:

According to basic proportionality theorem, if a line segment intersect the two sides and parallel to third side of the triangle, then it divides the two sides proportionally.

Using basic proportionality theorem, we get

$\dfrac{8}{20-8}=\dfrac{6}{x}$