9514 1404 393
Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

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Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
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* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).
Is it possible it’s (-2,2)
Find the perimeter of the polygon with the vertices g(2, 4), h(2,−3), j(−2,−3), g(2, 4), h(2,−3), j(−2,−3), and k(−2, 4)k(−2, 4)
Julli [10]
<span>The distance between g and h is sqrt[(2-2)^2+(4+3)^2]=7
The distance between h and j is sqrt[(2+2)^2+(-3+3)^2]=4
The distance between j and k is sqrt[(-2+2)^2+(-3-4)^2]=7
The distance between k and g is sqrt[(-2-2)^2+(4-4)^2]=4
The perimeter of the polygon is 7+4+7+4=22</span>
Answer:
y = 65°
Step-by-step explanation:
z = 70° (corresponding angels are equal)
y + z = 135° (exterior angle theorem of a triangle)
y + 70 = 135 (substitution)
Subtract 70 from each side
y + 70 - 70 = 135 - 70
y = 65
Answer:
3(x-1)
Step-by-step explanation:
12+3x-15
-3+3x
3(x-1)