Exploring Vertex: Finding the Maximum of y = -2x(x+1)

Does the parable

$y=-2x(x+1)$

Is there a minimum or maximum point?

To determine whether there is a minimum or maximum point in the quadratic function $y = -2x(x+1)$, let's follow these steps:

• Simplify the given function. Distribute the negative sign to expand the polynomial:

$y = -2x(x+1)$

$y = -2x^2 - 2x$

• Identify the coefficients of the quadratic equation in the form $ax^2 + bx + c$:
• $a = -2$, $b = -2$, and $c = 0$.
• Since the coefficient of $x^2$, $a$, is negative, the parabola opens downwards.

When a parabola opens downwards, it has a maximum point, as it reaches a peak value (the highest point) before descending.

Therefore, the quadratic function $y = -2x(x+1)$ has a maximum point.

Hence, the correct answer is that the parable has a highest point.