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Given the quadratic functions below, give the maximum or minimum value, the intercepts, and

state the range. Sketch each function.

a. F(x) = x2 – 1

b. F(x) = x(x+3) – 12

f(x) = x² - 1

This is the equation of a vertical parabola with vertex (0, -1). The coefficient of x² is positive, so the parabola opens upwards and the minimum value is -1. The range is [-1, ∞).

The y-intercept is the value of f(0) = -1.

The x-intercepts are the values of x for which f(x) = 0.

x² - 1 = 0

x = ±1

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