Question 453097: How do you know if the parabola opens upward or downward? What are 3 key points you can determine and graph from the equation? Demonstrate with an example.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do you know if the parabola opens upward or downward? What are 3 key points you can determine and graph from the equation? Demonstrate with an example.
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y = ax^2+bx+c
If "a" is positive, opens upward.
If "a" is negative, opens downward.
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3 key points:
2 x-intercepts or roots
1 y-intercept
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Example:
x intercepts: (2,0) and (5,0)
y intercept: (0,8)
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y = ax^2 + bx + c
Using (0,8) you know c = 8
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Using the x-intercepts:
0 = (x-2)(x-3)
0 = x^2-5x+6
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y = a(x^2-5x+6)
y = ax^2-5ax+6a
6a = 8
a = 4/3
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y = (4/3)x^2-(20/3)x+ (4/3)*6
y = (4/3)x^2-(20/3)x + 8
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Cheers,
Stan H.
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