23.03.2023 - 08:21

Rewrite the expression without using the absolute-value symbol. |1 – 2 x^2|

Question:

Rewrite the expression without using the absolute-value symbol.

{eq}\displaystyle left |1 – 2 x^2right | {/eq}

Answers (1)
  • Larue
    April 5, 2023 в 21:02
    The expression {eq}\displaystyle left |1 - 2 x^2right | {/eq} represents the distance between the point (x,1) and the x-axis on a coordinate plane. When x is positive, the point (x,1) is above the x-axis, and when x is negative, the point (x,1) is below the x-axis. In either case, the distance between the point and the x-axis is positive. Therefore, we can rewrite the expression as {eq}\displaystyle 1-2x^2 {/eq} if {eq}\displaystyle x^2leq \frac{1}{2} {/eq} and as {eq}\displaystyle 2x^2-1 {/eq} if {eq}\displaystyle x^2>frac{1}{2} {/eq}.
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