Problem:
The least value of the function ax2+bx+c with a>0 is:
Answer Choices:
A. βabβ
B. β2abβ
C. b2β4ac
D. 4a4acβb2β
E. none of the above.
Solution:
The graph of the function y=ax2+bx+c, for aξ =0, is a parabola with its axis of symmetry parallel to the y-axis.
We wish to find the coordinates of V. Let y=k be any line parallel to the x-axis which intersects the parabola at two points, say P and Q. Then the abscissa (the x-coordinate) of the midpoint of the line segment PQ is the abscissa of V. Since P and Q are the intersections of the line y=k with the parabola, the abscissas of P and Q must satisfy the equation
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