<h3>
Answers:</h3>
The first ordered pair is ( -4 , -3 )
The second ordered pair is ( 8, 3 )
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Explanation:
The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x
x-2y = 2
x-2(-3) = 2 ... replace every y with -3; isolate x
x+6 = 2
x = 2-6
x = -4
The first point is (-4, -3)
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We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y
x-2y = 2
8-2y = 2
-2y = 2-8
-2y = -6
y = -6/(-2)
y = 3
The second point is (8, 3)
The equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
<h3>How to determine the functions?</h3>
A quadratic function is represented as:
y = a(x - h)^2 + k
<u>Question #6</u>
The vertex of the graph is
(h, k) = (-1, 2)
So, we have:
y = a(x + 1)^2 + 2
The graph pass through the f(0) = -2
So, we have:
-2 = a(0 + 1)^2 + 2
Evaluate the like terms
a = -4
Substitute a = -4 in y = a(x + 1)^2 + 2
y = -4(x + 1)^2 + 2
<u>Question #7</u>
The vertex of the graph is
(h, k) = (2, 1)
So, we have:
y = a(x - 2)^2 + 1
The graph pass through (1, 3)
So, we have:
3 = a(1 - 2)^2 + 1
Evaluate the like terms
a = 2
Substitute a = 2 in y = a(x - 2)^2 + 1
y = 2(x - 2)^2 + 1
<u>Question #8</u>
The vertex of the graph is
(h, k) = (1, -2)
So, we have:
y = a(x - 1)^2 - 2
The graph pass through (0, -3)
So, we have:
-3 = a(0 - 1)^2 - 2
Evaluate the like terms
a = -1
Substitute a = -1 in y = a(x - 1)^2 - 2
y = -(x - 1)^2 - 2
Hence, the equations of the functions are y = -4(x + 1)^2 + 2, y = 2(x - 2)^2 + 1 and y = -(x - 1)^2 - 2
Read more about parabola at:
brainly.com/question/1480401
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The lengths of the bases would be 3 and 9
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