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Over [174]
3 years ago
12

A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, the

re is exactly one quadratic function whose graph contains these points. Find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17). Enter the equation below. Function: y = 0

Mathematics
1 answer:
pochemuha3 years ago
8 0

Answer:

The quadratic function whose graph contains these points is y=-x^{2}-2x-2

Step-by-step explanation:

We know that a quadratic function is a function of the form y=ax^{2}+bx+c. The first step is use the 3 points given to write 3 equations to find the values of the constants <em>a</em>,<em>b</em>, and <em>c</em>.  

Substitute the points (0,-2), (-5,-17), and (3,-17) into the general form of a quadratic function.

-2=a*0^{2}+b*0+c\\c=-2

-17=a*-5^{2}+b*-5+c\\c=-25a+5b-17

-17=a*3^{2}+b*3+c\\ c=-9a-3b-17

We can solve these system of equations by substitution

  • Substitute c=-9a-3b-17

-9a-3b-17=25a+5b-17\\-9a-3b-17=-2

  • Isolate a for the first equation

-9a-3b-17=-25a+5b-17\\a=\frac{b}{2}

  • Substitute a=\frac{b}{2} into the second equation

-9\left(-\frac{b}{2}\right)-3b-17=-2

  • Find the value of b

-9\left(-\frac{4b}{17}\right)-3b-17=-2\\ b=-2

  • Find the value of a

a=\frac{b}{2}\\  a=-1

The solutions to the system of equations are:

b=-2,a=-1,c=-2

So the quadratic function whose graph contains these points is

y=-x^{2}-2x-2

As you can corroborate with the graph of this function.

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uysha [10]

Answer:

Step-by-step explanation:

Given that that (X) the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.

i.e. X is normal with mean = 15 and unknown std deviation \sigma

Given thatP(X

i.e. P(z

z=-1.475 (from normal table)

Hence \frac{13-15}{\sigma}=-1.475\\\sigma = 1.356

Using this we find P(X>17) = P(Z>\frac{17-15}{1.356} \\=P(Z>1.475)\\=0.5-0.428\\=0.072

6 0
3 years ago
A train is traveling at 60 mph. If the rate of speed increases 4 mph each hour,
Alenkasestr [34]

Answer:

B) 5 hours

Step-by-step explanation:

First, find the amount of mph between 60 and 80:

80 - 60

= 20 mph

Since the speed increases 4 mph per hour, we can find how long it will take to get to 80 mph by dividing 20 by 4:

20/4

= 5

So, the correct answer is B, 5 hours

6 0
2 years ago
A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the
Andre45 [30]

Answer:

Option: B

There are three times as many participants in the 40-59 age group than in the 0-19 age group.

Step-by-step explanation:

From the histogram we have following observations:

Number of people in the age group  0-19= 20

Number of people in the age group 20-39=40

Number of people in the age group 40-59=60

Number of people in the age group 60-79=50

Hence, from the data we could say that  there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).

Hence, option B is correct.


4 0
3 years ago
Read 2 more answers
Use Gauss-Jordan elimination to solve the following linear system.
marysya [2.9K]
Just put the coefients in to a matrix

1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14

\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\-2&2&-3|-14\end{array}\right]
mulstiply 2nd row by -1 and add to 3rd
\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&2&0|-6\end{array}\right]
divde last row by 2
\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]
multiply 2rd row by 6 and add to top one
\left[\begin{array}{ccc}1&0&-3|-14\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]
multiply 1st row by -1 and add to 2nd
\left[\begin{array}{ccc}1&0&-3|-14\\-3&0&0|6\\0&1&0|-3\end{array}\right]
divide 2nd row by -3
\left[\begin{array}{ccc}1&0&-3|-14\\1&0&0|-2\\0&1&0|-3\end{array}\right]
mulstiply 2nd row by -1 and add to 1st row
\left[\begin{array}{ccc}0&0&-3|-12\\1&0&0|-2\\0&1&0|-3\end{array}\right]
divide 1st row by -3
\left[\begin{array}{ccc}0&0&1|4\\1&0&0|-2\\0&1&0|-3\end{array}\right]

rerange
\left[\begin{array}{ccc}1&0&0|-2\\0&1&0|-3\\0&0&1| 4\end{array}\right]

x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)

B is answer
7 0
2 years ago
I keep getting confused on this one
il63 [147K]

Answer:

he made the mistake on step one, he didn't distribute correctly

Step-by-step explanation:

-5(x-1) = -5x +5

not -5x - 1

6 0
2 years ago
Read 2 more answers
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