What are the coordinates of the circumcenter of a triangle with vertices A(−1, 1) , B(5, 1) , and C(−1, −1) ?
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Answer:
see explanation
Step-by-step explanation:
the equation of parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier.
here (h, k ) = (3, 1 ) , then
y = a(x - 3)² + 1
to find a substitute any other point on the graph into the equation.
using (0, 7 )
7 = a(0 - 3)² + 1 ( subtract 1 from both sides )
6 = a(- 3)² = 9a ( divide both sides by 9 )
=
= a
y = (x - 3)² + 1 ← in vertex form
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the equation of a parabola in factored form is
y = a(x - a)(x - b)
where a, b are the zeros and a is a multiplier
here zeros are - 1 and 3 , the factors are
(x - (- 1) ) and (x - 3), that is (x + 1) and (x - 3)
y = a(x + 1)(x - 3)
to find a substitute any other point that lies on the graph into the equation.
using (0, - 3 )
- 3 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
1 = a
y = (x + 1)(x - 3) ← in factored form
So. let's say the numbers are "a" and "b"
whatever they're, we know a + b = 56
let's say the larger one is "b", so 3 times the smaller is 3*a or 3a
now, 12 less than that, is 3a - 12
and the larger is that, so b = 3a - 12
so
solve for "a", to see what the smaller one is
what's b? well, b = 56 - a
whatever they're, we know a + b = 56
let's say the larger one is "b", so 3 times the smaller is 3*a or 3a
now, 12 less than that, is 3a - 12
and the larger is that, so b = 3a - 12
so
solve for "a", to see what the smaller one is
what's b? well, b = 56 - a