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Slav-nsk [51]
3 years ago
8

Bonus: 2 points for vertex form or standard form, 5 points for both

Mathematics
1 answer:
Vikki [24]3 years ago
4 0

9514 1404 393

Answer:

  • y = (x -3)² -5
  • y = x² -6x +4

Step-by-step explanation:

The vertex form of the quadratic equation is ...

  y = a(x -h)² +k . . . . . . . . . vertex (h, k); vertical scale factor 'a'

Given the vertex, we can find the scale factor by substituting the given point values:

  11 = a(-1 -3)² -5

  11 = 16a -5

  a = (11 +5)/16 = 1

So, the vertex form equation is ...

  y = (x -3)² -5 . . . . . vertex form

Expanding this gives the standard form.

  y = x² -6x +9 -5

  y = x² -6x +4 . . . . . standard form

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*25 points!*
mariarad [96]
Pick 2 pairs of equations t<span>hen use addition and subtraction to eliminate </span>the same variable<span> from both pairs of equations then it is left with 2 variables 
</span>Pick two pairs
<span><span>4x - 3y + z = - 10</span><span>2x + y + 3z = 0
</span></span>eliminate the same variable from each system
<span><span>4x - 3y + z = - 10</span> 
<span>2x + y + 3z = 0</span> 

<span>4x - 3y + z = - 10</span> 
<span>-4x - 2y - 6z = 0</span> 

<span>-5y - 5z = - 10</span> 

<span>2x + y + 3z = 0</span> 
<span>- x + 2y - 5z = 17</span> 

<span>2x + y + 3z = 0</span> 
<span>-2x + 4y - 10z = 34</span> 

<span>5y - 7z = 34
</span></span>Solve the system of the two new equations:
<span><span>-5y - 5z = - 10</span> 
<span>5y - 7z = 34</span> 

<span>-12z = 24</span> 
which is , <span>z = - 2</span> 

<span>-5y - 5(- 2) = - 10</span> 
<span>-5y = - 20</span> 
wich is , <span>y = 4
</span></span>substitute into one of the original equations
<span>- x + 2y - 5z = 17</span> 
<span>- x + 2(4) - 5(- 2) = 17</span> 
<span>- x + 18 = 17</span> 
<span>- x = - 1</span> 
<span>x = 1</span> 
<span>which is , </span><span>(x, y, z) = (1, 4, - 2)</span><span> 
</span>Does 2(1) + 4 + 3(- 2) = 0<span> ? Yes</span><span>

</span>
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ArbitrLikvidat [17]
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manny is on a bus that is traveling at a constant speed of 60 miles per hour. how far will he travel in 3 1/2 hours
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use this equation to solve for the surface area.

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Answer:

  see the attachment

Step-by-step explanation:

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