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Complete the tables and find the values of m and n for the function y = x2 − 1/4.

Mathematics

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Graph of y = x² − 1/4

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Key points of y = x² − 1/4
Pointxy
x-intercept−0.50
Minimum0−0.25
x-intercept0.50

Step-by-step solution

2 steps

Here are the completed tables and the values of mm and nn:

a) Function: y=x2−14y = x^2 - \frac{1}{4}

  1. Calculate yy for given xx values.

    For x=−2x = -2: y=(−2)2−14=4−14=154y = (-2)^2 - \frac{1}{4} = 4 - \frac{1}{4} = \frac{15}{4}
    For x=−1x = -1: y=(−1)2−14=1−14=34y = (-1)^2 - \frac{1}{4} = 1 - \frac{1}{4} = \frac{3}{4}
    For x=0x = 0: y=(0)2−14=0−14=−14y = (0)^2 - \frac{1}{4} = 0 - \frac{1}{4} = -\frac{1}{4}
    For x=1x = 1: y=(1)2−14=1−14=34y = (1)^2 - \frac{1}{4} = 1 - \frac{1}{4} = \frac{3}{4}
    For x=2x = 2: y=(2)2−14=4−14=154y = (2)^2 - \frac{1}{4} = 4 - \frac{1}{4} = \frac{15}{4}

  2. Solve for mm and

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