I forgot how to find the percent of decrease can someone please help?
1 answer:
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9514 1404 393
Answer:
y = -x^2 +3x -4
Step-by-step explanation:
We are given two points with the same y-value, so we know the axis of symmetry lies halfway between their x-coordinates, at ...
x = (1 +2)/2 = 3/2
Then the vertex form of the equation can be written ...
y = a(x -3/2)^2 +k
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We can use two of the points to find the values of 'a' and 'k'.
<u>For (x, y) = (1, -2)</u>
-2 = a(1 -3/2)^2 +k = a/4 +k
<u>For (x, y) = (3, -4)</u>
-4 = a(3 -3/2)^2 +k = 9a/4 +k
Subtracting the first of these equations from the second, we have ...
(9a/4 +k) -(a/4 +k) = (-4) -(-2)
2a = -2
a = -1
Then k can be found from the first equation.
-2 = -1/4 +k
k = -1 3/4
So, the vertex form equation is ...
y = -(x -3/2)^2 -7/4
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Expanding this, we can find the standard form.
y = -(x^2 -3x +9/4) -7/4)
y = -x^2 +3x -4
Answer:
(a) Similar polygons; scale factor is 2
(b) Similar polygons; scale factor is 1.5
Step-by-step explanation:
Given
See attachment for polygons
Required
Determine if they are similar or not
Solving (a): The triangle
The angles in both triangles show that the triangles are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
<em>The scale factor is 2</em>
<em />
Solving (b): The trapezium
The angles in both trapeziums show that the trapeziums are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
<em>The scale factor is 1.5</em>
