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(1) \( f(x)=x^{2}-1 \)

Ask by Wright Gray. in South Africa
Mar 16,2025

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The function \( f(x) = x^2 - 1 \) is a parabola opening upwards with a minimum value of \(-1\) at \( x = 0 \). Its domain is all real numbers, and its range is \( [-1, \infty) \). It has y-intercept at \( (0, -1) \) and x-intercepts at \( (1, 0) \) and \( (-1, 0) \).

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Mind Expander

Did you know that quadratic functions, like \( f(x) = x^2 - 1 \), can be graphed as parabolas? This specific function opens upwards and its vertex is located at the point \( (0, -1) \). The parabola will cross the x-axis at points where \( x^2 - 1 = 0 \), which means the x-intercepts are \( x = 1 \) and \( x = -1 \). In real-world scenarios, quadratic functions can model a wide variety of phenomena, including projectile motion. For example, if you were to throw a ball, its path can be described by a quadratic function similar to this one, illustrating how height changes over time. Imagine plotting its trajectory and predicting at what point it will hit the ground!

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