A school quiz cmon guys
1 answer:
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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:
_____
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
_____
* 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).
Answer:
<u>Translate K to N and reflect across the line containing JK. </u>
Step-by-step explanation:
The rest of the question is the attached figure.
From the figure, we can deduce the following:
∠K = ∠N
JK = MN
HK = LN
So, N will be the image of K
By translating K to N, The segment JK will over-lap the segment MN,
Then, we need to reflect the point H across the the line containing JK to get the point L
So, the translation and a reflection that will be used to map ΔHJK to ΔLMN:
<u>Translate K to N and reflect across the line containing JK. </u>
