Question

Find the maximum or minimum of the function.

y = −x2 − 6x

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the maximum or minimum of the function y = -x^2 - 6x, we first need to determine whether the function is facing upwards or downwards. Since the coefficient of the x^2 term is negative (-1), the parabola opens downwards.

The vertex of the parabola represents either the maximum point if the parabola opens downwards, or the minimum point if the parabola opens upwards. To find the vertex, we can use the formula for the x-coordinate of the vertex in terms of the coefficients of the quadratic function: x = -b/(2a), where the function is in the form y = ax^2 + bx + c.

In this case, a = -1 and b = -6. Substituting into the formula, we get x = -(-6)/(2*-1) = 6/-2 = -3.

Now that we have the x-coordinate of the vertex (-3), we can find the y-coordinate by substituting this value back into the original function:

y = -(-3)^2 - 6(-3)
y = -9 + 18
y = 9

Therefore, the vertex of the parabola is at (-3, 9), which represents the minimum value of the function y = -x^2 - 6x.