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Nuetrik [128]
3 years ago
5

Write a quadratic equation with the given vertex.​

Mathematics
1 answer:
timurjin [86]3 years ago
4 0

Answer:

See below

Step-by-step explanation:

14. \: vertex \: ( - 4, \:  - 3) \\ require \: quadratic \: equation \\  {x}^{2}  - ( - 4 - 3)x + ( - 4)( - 3) = 0 \\  {x}^{2}  + 7x + 12 = 0 \\  \\ 15. \: vertex \: ( - 2, \:  1) \\ require \: quadratic \: equation \\  {x}^{2}  - ( - 2  + 1)x + ( - 2)( 1) = 0 \\  {x}^{2}  + x  - 2 = 0\\  \\ 16. \: vertex \: ( 3, \:  8) \\ require \: quadratic \: equation \\  {x}^{2}  - ( 3  + 8)x + (3)( 8) = 0 \\  {x}^{2}  + 11x  - 24 = 0

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The graph of a sinusoidal function intersects its midline at (0,5) and then has a maximum point at (\pi,6)
lesya692 [45]
First, let's use the given information to determine the function's amplitude, midline, and period. 

Then, we should determine whether to use a sine or a cosine function, based on the point where x=0.

Finally, we should determine the parameters of the function's formula by considering all the above.
     
                      Determining the amplitude, midline, and period 

The midline intersection is at y=5 so this is the midline. 

The maximum point is 1 unit above the midline, so the amplitude is 1. 

The maximum point is π units to the right of the midline intersection, so the period is 4 * π.
 
                            Determining the type of function to use 

Since the graph intersects its midline at x=0, we should use thesine function and not the cosine function. 

This means there's no horizontal shift, so the function is of the form -

a sin(bx)+d

Since the midline intersection at x=0 is followed by a maximumpoint, we know that a > 0.

The amplitude is 1, so |a| = 1. Since a >0 we can conclude that a=1. 

The midline is y=5, so d=5. 

The period is 4π so b = 2π / 4π = 1/2 simplified. 

f(x) = 1 sin ( \dfrac{1}{2}x)+5   <span>= Solution </span>
4 0
3 years ago
A circuit board manufacturer can produce 2,000 boards per hour. How many days will it take to produce 16,500 if the company has
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5 0
3 years ago
Read 2 more answers
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zubka84 [21]
<u>The possible answers are:
</u>
<u /><u /><u><em /></u>4.21
4.22
4.23
4.24

Explanation:
We want a number between 4 1/5 and 4.25.  We will convert 4 1/5 to a decimal first:

Divide 1 by 5:  1/5 = 0.2.

This makes 4 1/5 = 4 + 1/5 = 4 + 0.2 = 4.2.

We want a number between 4.2, which can be written as 4.20, and 4.25.  Any number between will do, so the possible answers would be 
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7 0
3 years ago
Read 2 more answers
-5x-y= 8<br> -4x+y=2 solve the system
yan [13]

\huge\fcolorbox{blue}{aqua}{Answer:}

═════════════════════

1.- 5x - y = 8

<h3>Solve for x</h3>

-5x-y=8

-5x=8+y

-5x=y+8

\frac{-5x}{-5}=\frac{y+8}{-5}

x=\frac{y+8}{-5}

x=\frac{-y-8}{5}

<h3>Solve for y</h3>

-5x-y=8

-y=8+5x

-y=5x+8

\frac{-y}{-1}=\frac{5x+8}{-1}

y=\frac{5x+8}{-1}

y=-5x-8

────────────────────

2.-4x-y=2

<h3>Solve for x</h3>

-4x-y=2

-4x=2+y

-4x=y+2

\frac{-4x}{-4}=\frac{y+2}{-4}

x=\frac{y+2}{-4}

x=-\frac{y}{4}-\frac{1}{2}

<h3>Solve for y</h3>

-4x-y=2

-y=2+4x

-y=4x+2

\frac{-y}{-1}=\frac{4x+2}{-1}

y=\frac{4x+2}{-1}

y=-4x-2

════════════════════

Explanation:

#Carry on learning

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2 years ago
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