Question 941453: chart which shows at least three ordered pairs for the function
y = x^2 - 2x + 2 Found 2 solutions by TimothyLamb, MathTherapy:Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! y = x^2 - 2x + 2
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find the roots:
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x^2 - 2x + 2 = 0
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the above quadratic equation is in standard form, with a=1, b=-2 and c=2
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1 -2 2
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the quadratic has two complex roots at:
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y = 1 + (1)i
y = 1 - (1)i
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therefore the function does not intersect the x-axis:
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however, the function has a vertex minimum at: (1, 1)
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two other points on the function are:
x = 0
y = 2
(0, 2)
and
x = 2
y = 2
(2, 2)
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the graph:
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STEP 1:
Find the coordinates of the vertex
The x-coordinate of the vertex or the axis of symmetry is at: __________ ------ Substituting 1 for x
y = 1 - 2 + 2
y, or the y-coordinate of the vertex = 1
1st point: Vertex: STEP 2:
We can now use 0 (1 less than axis of symmetry value) for x to determine the y value.
Incidentally, this is the Y-INTERCEPT of the parabola ------ Substituting 0 for x
2nd point: y-intercept: STEP 3:
As all parabolas are symmetrical about the vertex, we can now use 2 (1 more than axis of symmetry value) for x to
determine the y value. The y-value for x = 2 will in this case, be the same y-value when x = 0 was substituted.
3rd point:
