What are the zeroes of the function? Graph the function.

y = x(x + 2)(x + 5)

1 answer

To find the zeroes of the function, we set y = 0 and solve for x:

0 = x(x + 2)(x + 5)

Since the equation is already factored, we can set each factor equal to zero:

x = 0, x + 2 = 0, x + 5 = 0

Solving for x gives us:

x = 0, x = -2, x = -5

Therefore, the zeroes of the function are x = 0, x = -2, and x = -5.

To graph the function, we can plot a few points and sketch the curve. Since the function is a cubic polynomial, we know it will have an "S" shape.

When x = 0, y = 0(0 + 2)(0 + 5) = 0. So we have the point (0, 0).

When x = -1, y = -1(-1 + 2)(-1 + 5) = 6. So we have the point (-1, 6).

When x = -3, y = -3(-3 + 2)(-3 + 5) = 24. So we have the point (-3, 24).

When x = -6, y = -6(-6 + 2)(-6 + 5) = -48. So we have the point (-6, -48).

Using these points, we can sketch the curve:

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-6 -5 -2 0 24

As the curve approaches x = -∞, it approaches negative infinity. As it approaches x = +∞, it approaches positive infinity.