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

Does the parable

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

Is there a minimum or maximum point?

Video Solution

Solution Steps

00:00 Does the parabola have a maximum or minimum point?

00:04 Let's properly open the brackets and multiply by each factor

00:18 The coefficient A of the function is negative, therefore the parabola is sad

00:23 Therefore the parabola has a maximum point

00:26 And this is the solution to the question

Step-by-Step Solution

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.