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

Q: Why do I need to expand y = 2x(x+3) first?

Expanding helps you clearly see the standard form y = ax² + bx + c. From y = 2x² + 6x, you can easily identify that a = 2, which tells you the parabola opens upward.

Q: What if the coefficient of x² is negative?

If a downward and has a maximum point at the vertex. Remember: positive a = minimum, negative a = maximum!

Q: How do I remember which direction the parabola opens?

Think of a smile and a frown! When a > 0, the parabola smiles (opens up) with a minimum point. When a

Q: Do I need to find the actual vertex coordinates?

Not for this question! You only need to determine if it's a minimum or maximum. The sign of the coefficient a tells you everything you need to know.

Q: What if there's no x² term visible?

Every quadratic must have an x² term! If you don't see one after expanding, double-check your work. The function y = 2x(x+3) definitely becomes $ y = 2x^2 + 6x $.

Quadratic Functions with Vertex Classification

Does the parable

$y=2x(x+3)$

Is there a minimum or maximum point?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Does the parable

$y=2x(x+3)$

Is there a minimum or maximum point?

Step-by-step solution

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.

Final Answer

Minimal point

Key Points to Remember

Essential concepts to master this topic

Rule: Coefficient of x² determines if parabola opens up or down
Technique: Expand 2x(x+3) = 2x² + 6x, coefficient a = 2
Check: Since a = 2 > 0, parabola opens upward = minimum point ✓

Common Mistakes

Avoid these frequent errors

Forgetting to expand the factored form before identifying coefficients
Don't try to find the coefficient from y = 2x(x+3) directly = confusion about which number is 'a'! You need the standard form ax² + bx + c to identify coefficients clearly. Always expand first to get y = 2x² + 6x, then identify a = 2.

Practice Quiz

Test your knowledge with interactive questions

Identify the coefficients based on the following equation

$$ y=x^2 $$

FAQ

Everything you need to know about this question

Why do I need to expand y = 2x(x+3) first?

Expanding helps you clearly see the standard form y = ax² + bx + c. From y = 2x² + 6x, you can easily identify that a = 2, which tells you the parabola opens upward.

What if the coefficient of x² is negative?

If a < 0 (negative), the parabola opens downward and has a maximum point at the vertex. Remember: positive a = minimum, negative a = maximum!

How do I remember which direction the parabola opens?

Think of a smile and a frown! When a > 0, the parabola smiles (opens up) with a minimum point. When a < 0, it frowns (opens down) with a maximum point.

Do I need to find the actual vertex coordinates?

Not for this question! You only need to determine if it's a minimum or maximum. The sign of the coefficient a tells you everything you need to know.

What if there's no x² term visible?

Every quadratic must have an x² term! If you don't see one after expanding, double-check your work. The function y = 2x(x+3) definitely becomes $y = 2x^2 + 6x$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime