A few days ago

# Functions and graphs?

A Quadratic function is given by f(x) = x² – 2x -3

a) Find values for the function when -2 ≤ x ≤ 4

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A few days ago

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You should be able to see that it’s a parabola, opening upwards. It factors as f(x) = (x – 3)(x + 1), so the zeros are at x = -1 and x = 3, putting the vertex at (-1 + 3)/2 = 1. That makes the vertex (1, -4).

If we’re looking for the values on [-2, 4], we know the vertex falls in that range. Therefore, the minimum value in there is -4, that being the vertex. The maximum value will be either f(-2) or f(4).

f(-2) = 4 + 4 – 3 = -3

f(4) = 16 – 8 – 3 = 5

So the maximum value in that interval will be 5. Therefore, the values on the interval [-2, 4] will be [-4, 5]

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