Determining the Vertex in the Quadratic Equation: y = 2x(x+3)

Question

Does the parable

$y=2x(x+3)$

Is there a minimum or maximum point?

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

00:03 Let's expand the brackets properly, multiply by each factor

00:19 The coefficient A of the function is positive, therefore the parabola smiles

00:22 Which means the parabola has a minimum point

00:26 And this is the solution to the question

To solve this problem, follow these steps:

Step 1: Express the quadratic function in standard form. The given function is $y = 2x(x + 3)$ , which can be expanded to $y = 2x^2 + 6x$ .
Step 2: Identify the coefficient of $x^2$ . In this case, $a = 2$ .
Step 3: Determine the direction of the parabola. Since $a = 2$ is positive, the parabola opens upwards.
Step 4: Conclude that the vertex represents the lowest point, which is the minimum point.

Given that the coefficient $a$ is positive, the parabola opens upwards, indicating that the vertex is a minimum point.

Therefore, the solution to this problem is minimal point.

Minimal point