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Temka [501]
3 years ago
11

Diagram below shows the curve of a quadratic function

Mathematics
1 answer:
uranmaximum [27]3 years ago
3 0

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of  -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The  r  is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

=  -6.

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the value of painting increases each year. To find the value of the painting for the next year, the art dealer multiplies the current value by 1.6. if the original value of the painting is 100, what is the value of the painting next yearStep-by-step explanation:


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2 years ago
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Step-by-step explanation:

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4 0
2 years ago
Answers should be exact decimals (please do not leave as fractions or unfinished calculations).
aksik [14]

Answer:

P(rolling the die results in a 3 or a 6)=0.3333

P(rolling the die results in not getting a 6)=0.8333

P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333

P(rolling the die results in an even number or a 5)=0.6667

P( rolling the die twice results in a 6 followed by a 4)=0.0278

P(rolling the die three times results in all 6's)=0.0046

Step-by-step explanation:

a)

As the all outcomes are equally likely, so each number has equal probability of occurring.

For six sided die the sample space is {1,2,3,4,5,6} and each outcome has equal probability of 1/6.

1)

P(rolling the die results in a 3 or a 6)

P(rolling the die results in a 3 or a 6)=P(3)+P(6)=1/6+1/6=2/6=1/3

P(rolling the die results in a 3 or a 6)=0.3333

P(rolling the die results in not getting a 6)

P(rolling the die results in not getting a 6)=1-P(6)=1-1/6=5/6

P(rolling the die results in not getting a 6)=0.8333

P(rolling the die results in the number being either greater than 2 or less than 5)

number either greater than 2 or less than 5={3,4}

P(rolling the die results in the number being either greater than 2 or less than 5)=2/6=1/3

P(rolling the die results in the number being either greater than 2 or less than 5)=0.3333

P(rolling the die results in an even number or a 5)

number is an even number or a 5={2,4,5,6}

P(rolling the die results in an even number or a 5)=4/6=2/3

P(rolling the die results in an even number or a 5)=0.6667

P( rolling the die twice results in a 6 followed by a 4)

For six sided die rolled twice the sample space is

S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}.

n(S)=6²=36.

rolling the die twice results in a 6 followed by a 4={(6,4)}

P( rolling the die twice results in a 6 followed by a 4)=1/36.

P( rolling the die twice results in a 6 followed by a 4)=0.0278

P(rolling the die three times results in all 6's)

When three die are rolled the number of outcomes=n(S)=6³=216.

rolling the die three times results in all 6's={(6,6,6)}

P(rolling the die three times results in all 6's)=1/216

P(rolling the die three times results in all 6's)=0.0046

Note: All answers are rounded to four decimal places.

8 0
3 years ago
What is the y-intercept of the exponential function? y=2(3)^x
ValentinkaMS [17]

Answer:

( 0 , 2 )

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y .

x-intercept(s): None

y-intercept(s): ( 0 , 2 )

3 0
3 years ago
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