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slega [8]
3 years ago
14

For the equation y=3x^2−6x−5, find the vertex showing all work.

Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
7 0

Answer:

<u>vertex:</u> (1, –8)

Step-by-step explanation:

a=3 \\b=-6\\c=-5

rewrite equation in vertex form: y=a(x-h)^2+k

1. factor out 3

y=3x^{2} -6x-5\\y=3(x^{2}-2x)-5\\  

2. complete the square using (\frac{b}{2} )^{2}:

(\frac{-2}{2})^2=1

3. add the answer from step 2 to inside the parenthesis to create a factorable trinomial. subtract the answer from step 2 from –5 and multiply it by a. remember: a = 3

y=3(x^{2} -2x+1)-5-1(3)\\y=3(x-1)(x-1)-8\\y=3(x-1)^2-8

4. find vertex

x-1=0\\x=1       y=-8

vertex = (1,-8)

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Step-by-step explanation:

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36 minus 15 equals 21.

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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
s2008m [1.1K]

Answer: 912

===================================

Work Shown:

The starting term is a1 = 3. The common difference is d = 5 (since we add 5 to each term to get the next term). The nth term formula is

an = a1+d(n-1)

an = 3+5(n-1)

an = 3+5n-5

an = 5n-2

Plug n = 19 into the formula to find the 19th term

an = 5n-2

a19 = 5*19-2

a19 = 95-2

a19 = 93

Add the first and nineteenth terms (a1 = 3 and a19 = 93) to get a1+a19 = 3+93 = 96

Multiply this by n/2 = 19/2 = 9.5 to get the final answer

96*9.5 = 912

I used the formula

Sn = (n/2)*(a1 + an)

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-----------------

As a check, here are the 19 terms listed out and added up. We get 912 like expected.

3+8+13+18   +23+28+33+38    +43+48+53+58    +63+68+73+78   +83+88+93 = 912

There are 19 values being added up in that equation above. I used spaces to help group the values (groups of four; except the last group which is 3 values) so it's a bit more readable.

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Answer:

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-z          -z

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z - 11 = 50

Add 11 to both sides:

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