What is the slope of the chord C between the points (–1, f(–1)) and (2, f(2))?
If one endpoint is (–1/2, f(–1/2)), what is the other endpoint of a chord that is parallel to C?
The chord has slope = (f(2) - f(-1))/(2 - (-1)) = (-2 + 0.5)/3 = –0.5
Therefore slope = –0.5
To find the other endpoint, we first obtain the equation of the chord and then equate it to f(x) to find out where it intersects the graph of f(x).
Using the point-slope form, y - y0 = m(x - x0), where m = –0.5, x0 = -1/2 and y0 = f(-1/2) = 1/8, we arrive at the equation y = (-1/2)x - 3/8
We now equate this expression to f(x) = (-1/2)x2
(-1/2)x - 3/8 = (-1/2)x2 => (x + 1/2)(x - 3/2) = 0 => x = -0.5 and 1.5
f(1.5) = -1.125, therefore endpoint = (1.5, –1.125)
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