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3 years ago

Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).

Mathematics

1 answer:

JulsSmile [24]3 years ago

3 0

Answer:

f(x) = 9(x -1/3)^2 -3

Step-by-step explanation:

In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...

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

To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":

1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given

1 = (4/9)a -3 . . . . simplify

4 = (4/9)a . . . . . . add 3

9 = a . . . . . . . . . . multiply by 9/4

The quadratic function you desire is ...

f(x) = 9(x -1/3)^2 -3

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Maria buys 4 1/5 pounds of plums. The total cost after using the coupon for 55 cents off her entire purchase is 3.23$. If c repr

Rudik [331]

$3.23 = 4 1/5c - .55

4 1/5c = the pounds of plums, and the cost of each pound. - .55 represents subtracting the coupon.

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3 years ago

Which set of ordered pairs does not represent a function?

Leokris [45]

The last one does not represent a function because for it to be a function none of the x’s can repeat and in the last one the 0 repeats.

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2 years ago

A box contains 11 red chips and 4 blue chips. We perform the following two-step experiment: (1) First, a chip is selected at ran

Scilla [17]

Answer:

P(B1) = (11/15)

P(B2) = (4/15)

P(A) = (11/15)

P(B1|A) = (5/7)

P(B2|A) = (2/7)

Step-by-step explanation:

There are 11 red chips and 4 blue chips in a box. Two chips are selected one after the other at random and without replacement from the box.

B1 is the event that the chip removed from the box at the first step of the experiment is red.

B2 is the event that the chip removed from the box at the first step of the experiment is blue. A is the event that the chip selected from the box at the second step of the experiment is red.

Note that the probability of an event is the number of elements in that event divided by the Total number of elements in the sample space.

P(E) = n(E) ÷ n(S)

P(B1) = probability that the first chip selected is a red chip = (11/15)

P(B2) = probability that the first chip selected is a blue chip = (4/15)

P(A) = probability that the second chip selected is a red chip

P(A) = P(B1 n A) + P(B2 n A) (Since events B1 and B2 are mutually exclusive)

P(B1 n A) = (11/15) × (10/14) = (11/21)

P(B2 n A) = (4/15) × (11/14) = (22/105)

P(A) = (11/21) + (22/105) = (77/105) = (11/15)

P(B1|A) = probability that the first chip selected is a red chip given that the second chip selected is a red chip

The conditional probability, P(X|Y) is given mathematically as

P(X|Y) = P(X n Y) ÷ P(Y)

So, P(B1|A) = P(B1 n A) ÷ P(A)

P(B1 n A) = (11/15) × (10/14) = (11/21)

P(A) = (11/15)

P(B1|A) = (11/21) ÷ (11/15) = (15/21) = (5/7)

P(B2|A) = probability that the first chip selected is a blue chip given that the second chip selected is a red chip

P(B2|A) = P(B2 n A) ÷ P(A)

P(B2 n A) = (4/15) × (11/14) = (22/105)

P(A) = (11/15)

P(B2|A) = (22/105) ÷ (11/15) = (2/7)

Hope this Helps!!!

5 0

3 years ago

Complete two ratios to describe the model. 4 dark blue triangles and 12 light blue triangles. The ratio of light blue triangles

____ [38]

Answer:

1:3

Step-by-step explanation:

4:12 simplified is 1:3. for every 1 dark blue there are 3 light blues.

5 0

3 years ago

Read 2 more answers

If f(x)=2x+5 , determine the value of f(3x) .

makvit [3.9K]

Answer:

Step-by-step ef(x)=-2x+5……i

and f(-3x)=?

let x=-3x so that

-2x+5=-3x

x=5

substitutinx x into… i

f(x)=-10+5=-5

f(5)=-5………ii

now f(–3x)=f(-15)

scrutinizing… ii ,we can propose that

f(-15)=15.

Thus f(-3x)=15xplanation:

7 0

2 years ago

Read 2 more answers