Analyzing Maximum or Minimum in the Parabola: y = -(x+1)(x-1)

Question

Does the parable

y=(x+1)(x1) y=-(x+1)(x-1)

Is there a minimum or maximum point?

Video Solution

Solution Steps

00:00 Does the parabola have a maximum or minimum point?
00:03 We'll use the shortened multiplication formulas and expand the brackets
00:12 Negative times positive is always negative
00:15 Negative times negative is always positive
00:21 The coefficient A of the function is negative, therefore the parabola is sad
00:24 Therefore the parabola has a maximum point
00:28 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's analyze the function step-by-step:

Step 1: Expand the given quadratic function.
The function provided is y=(x+1)(x1) y = -(x+1)(x-1) . We rewrite it by expanding:

y=(x21)=x2+1 y = -(x^2 - 1) = -x^2 + 1 .

Step 2: Determine the direction of the parabola.
The standard form y=ax2+bx+c y = ax^2 + bx + c indicates that the parabola opens upwards if a>0 a > 0 and downwards if a<0 a < 0 . Here, the value of a a is 1-1, which means the parabola opens downwards.

Step 3: Identify the vertex type.
Since the parabola opens downwards, the vertex represents the highest point on the graph, which is a maximum.

Therefore, the parabola has a maximum point. The correct choice is:

Choice 2: Highest point

Thus, we conclude that the given quadratic function has a maximum point.

Answer

Highest point