Sketch the curve y = 2x^2 - 4x + 1, indicating the coordinates of the turning point
and the exact values of the x-intercepts. Hence find
(a) the set of values of x for which 2x^2 + 1 ≥ 4x,
(b) the range of values of p if 2x^2 - 4x + 1 + p = 0 has no real roots.
Please help, thank you in advance.
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Step-by-step explanation:
The parabola is a curve that was known and studied in antiquity. It arises from the dissection of an upright cone.
With the advent of coordinate geometry, the parabola arose naturally as the graph of a quadratic function. The graph of the function y = mx + b is a straight line and the graph of the quadratic function y = ax2 + bx + c is a parabola. Since y = mx + b is an equation of degree one, the quadratic function, y = ax2 + bx + c represents the next level of algebraic complexity.
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