Given the quadratic relation y = -x2 + 6x - 6, a) write the equation in vertex form b) graph the quadratic relation (using noteb
ook, Google Drawings, or by hand) using transformations on y = x2. Insert your graph image (or link) here.
I am pretty sure that for this one vertex form is -(x-3)^2+3
Double check that answer and then graph it please!
I am pretty sure that for this one vertex form is -(x-3)^2+3
Double check that answer and then graph it please!
1 answer:
<h3>Answer:</h3>
- y = -(x -3)² +3 . . . . (agrees with your answer)
- see the attachment for a graph
Factoring the leading -1 from the first two terms, we have ...
... y = -(x² -6x) -6
Adding 9 inside parentheses to complete the square, then adding the opposite amount outside parentheses, we have ...
... y = -(x² -6x +9) -6 +9
... y = -(x -3)² +3
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Interchange the x and y and solve for the resulting y.
x = 4y^2 - 2
(x + 2) = 4y^2
(x + 2)/4 = y^2
+/- sqrt(x + 2)/2 = y
The graph of these two is below.
The original is in red
The inverse is in blue and green
x = 4y^2 - 2
(x + 2) = 4y^2
(x + 2)/4 = y^2
+/- sqrt(x + 2)/2 = y
The graph of these two is below.
The original is in red
The inverse is in blue and green