Parabola and its Vertex Remember, parabolas have equations : The Standard Form for a parabola :
REVIEW y = ax2 + bx + c is a parabola. If a 0, the parabola is oriented upward and the vertex is...
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REVIEW y = ax2 + bx + c is a parabola. If a > 0 , the parabola is oriented upward and the vertex is the minimum point of the function. If a < 0 , the parabola is oriented downward and the vertex is the maximum point of the function. In either case the vertex of the parabola is located halfway between the roots (the zeros or x-intercepts.) The x-coordinate of the vertex can be found by substituting the x-value of the vertex into the equation of the function that yields the y-value of the vertex. The quadratic function may be given or it may need to be created based on the given information of the situation.
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Example 2 With 100 feet of fence, what are the dimensions of the corral of largest area that a farmer can create if his barn will provide one side of the corral? Let x = the width of the corral and then x is the length. The function which represents the area is y = ( x)x = -2x x The corral of maximum area has width x = 25 feet, length 50 feet, and area 1250 ft 2 W.S. Problems: 1, 2, 5,
Transcript of REVIEW y = ax2 + bx + c is a parabola. If a 0, the parabola is oriented upward and the vertex is...
REVIEWy = ax2 + bx + c is a parabola.
If a > 0 , the parabola is oriented upward and the vertex is the minimum point of the function.
If a < 0 , the parabola is oriented downward and the vertex is the maximum point of the function.
In either case the vertex of the parabola is located halfway between the roots (the zeros or x-intercepts.)
The x-coordinate of the vertex can be found by substituting the x-value of the vertex into the equation of the function that yields the y-value of the vertex.
The quadratic function may be given or it may need to be created based on the given information of the situation.
Example 1What is the minimum value of the function-8x-5?
The x-coordinate of the vertex is =
The y-coordinate of thevertex is y
The coordinates of the vertex are (2, -13) and theminimum value of the function is –13.
Example 2With 100 feet of fence, what are the dimensions of the corral of largest area that a farmercan create if his barn will provide one side of the corral?
Let x = the width of the corral and then 100 - 2x is the length.
The function which representsthe area is y = (100 - 2x)x = -2x2 + 100xThe vertex of this function is at = andy = -2(25)2 + 100(25) = 1250
The corral of maximum area has width x = 25 feet, length 50 feet, and area 1250 ft2
W.S. Problems: 1, 2, 5,
