Write a quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, −17) .
1 answer:
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Answer:
A)segment A"B"= AB / 2
Step-by-step explanation:
Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. Which equation explains the relationship between segment AB and segment A"B"?
coordinate plane with triangle ABC at A(-3, 3), B(1, -3), and C(-3, -3)
A)segment A"B"= AB / 2
B)segment AB = segment A"B"/ 2
C)segment AB / segment A"B"= 1/2
D)segment A"B" / segment AB = 2
A"B" = AB / 2
Because
1. translations do not change the lengths of segments, so (x+2, y+0) preserves the length of AB, i.e. mA'B' = mAB
2. Dilation causes the new segment to be transformed to a new length according to the old length * the scale factor of (1/2).
Therefore A"B" = (1/2)AB, or AB/2.
Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.