Answer:
f(x) = (x -6)² +14
Step-by-step explanation:
Completing the square involves writing part of the function as a perfect square trinomial.
<h3>Perfect square trinomial</h3>
The square of a binomial results in a perfect square trinomial:
(x -h)² = x² -2hx +h²
The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².
<h3>Completing the square</h3>
One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.
Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...
f(x) = x² -12x +36 +50 -36
Rearranging into the desired form, this is ...
f(x) = (x -6)² +14
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<em>Additional comment</em>
Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.
f(x) = x² -12x +(36 +14)
f(x) = (x² -12x +36) +14
f(x) = (x -6)² +14
T<span>he number of questions Natalie answered incorrectly.</span>
Answer:
1
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (5-8)/(-8 - -5)
= -3/(-8+5)
= -3/-3
= 1
Answer:
18793000
Step-by-step explanation:
Answer:
Angle R is 99 degree
Angle Y=48 degrees
Angle T is 33 degrees
Step-by-step explanation:
Let angle T be x
Angle R will be 3x
Angle Y will be x+15
Total=x+3x+x+15=5x+15
5x+15=180
5x=165
x=165/5=33
Therefore, angle T is 33 degrees, angle Y=15+33=48 degrees and angle R=33*3=99 degrees
