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What information can the coefficients a, b, and c give you?
Vertex: (2/3,- 3 13)
Axis of Symmetry: x=2/3
Minimum Value: -3 13
Range: -3 13 ≤ y < ∞
Consider the point at which the curve of the parabola changes direction.
The point at which the graph of a parabola changes direction also defines the maximum or minimum point of the graph. Whether the parabola has a minimum or maximum is determined by the value of a.
x= 2/3
(a/b)^m=a^m/b^m
a*b/c= a* b/c
a/b=.a /3./.b /3.
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Given the standard form of a parabola, the ( x, y) coordinates of its vertex can be expressed in terms of a and b. ( x, y) ⇔ ( - b/2 a, f(- b/2 a ) ) We have already calculated both of these values above, so we know that the vertex lies on the point ( 23, -3 13).
One common mistake when identifying the key features of a parabola algebraically is forgetting to include the negatives in the values of these constants. The standard form is addition only, so any subtraction must be treated as negative values of a, b, or c. Let's look at an example. y=3x^2-4x-2 ⇕ y=3x^2 + (-4x) + (-2) In this case, the values of a, b, and c are 3, -4, and -2. They are NOT 3, 4, and 2. a=3, b=4, c=2 * a=3, b=-4, c=-2 ✓