Pinpoint the Vertex of the Quadratic Function: y = x² + 3

Q: Why is the vertex at (0,3) and not (3,0)?

The vertex has x-coordinate first, then y-coordinate. Using the formula x = -b/(2a) with b = 0 gives x = 0. Then substituting: y = (0)² + 3 = 3. So the vertex is (0,3).

Q: What does it mean when b = 0 in a quadratic?

When b = 0, there's no x-term in the equation. This means the parabola is perfectly centered on the y-axis, so the vertex always has x-coordinate = 0.

Q: How do I remember the vertex formula?

Think of it as "negative b over 2a": $ x = -\frac{b}{2a} $. The negative sign is crucial - don't forget it!

Q: Is this parabola opening up or down?

Since a = 1 > 0, this parabola opens upward. The vertex (0,3) is the lowest point on the graph.

Q: What if I get confused about which coordinate is which?

Remember: (x, y) means "across, then up". The first number is how far left or right, the second is how far up or down from the origin.

Vertex Form with Constant Terms

Find the vertex of the parabola

$y=x^2+3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the vertex of the parabola

00:03 Use the formula to describe the parabola function

00:07 The coordinates of the vertex are (P,K)

00:13 Use this formula and find the vertex point

00:24 Substitute appropriate values according to the given data

00:27 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

Find the vertex of the parabola

$y=x^2+3$

Step-by-step solution

To solve for the vertex of the parabola given by the equation $y = x^2 + 3$ , we will follow these steps:

Step 1: Identify the coefficients from the equation. We have $a = 1$ , $b = 0$ , and $c = 3$ .
Step 2: Calculate the x-coordinate of the vertex using the formula $x = -\frac{b}{2a}$ . Since $b = 0$ , the formula becomes $x = -\frac{0}{2 \times 1} = 0$ .
Step 3: Find the y-coordinate of the vertex by substituting $x = 0$ back into the equation. Calculate $y = (0)^2 + 3 = 3$ .

Therefore, the vertex of the parabola is at the point $(0, 3)$ .

This corresponds to choice 3: $(0,3)$ .

Final Answer

$(0,3)$

Key Points to Remember

Essential concepts to master this topic

Vertex Formula: Use x = -b/(2a) to find x-coordinate of vertex
Technique: When b = 0, vertex x-coordinate is always x = 0
Check: Substitute x = 0 back: y = (0)² + 3 = 3 gives (0,3) ✓

Common Mistakes

Avoid these frequent errors

Confusing vertex coordinates with y-intercept
Don't think the vertex is (3,0) just because the constant is 3! This mixes up coordinates and gives the wrong point. Always use the vertex formula x = -b/(2a), then substitute to find y-coordinate.

Practice Quiz

Test your knowledge with interactive questions

The following function has been plotted on the graph below:

$$ f(x)=x^2-8x+16 $$

Calculate point C.

FAQ

Everything you need to know about this question

Why is the vertex at (0,3) and not (3,0)?

The vertex has x-coordinate first, then y-coordinate. Using the formula x = -b/(2a) with b = 0 gives x = 0. Then substituting: y = (0)² + 3 = 3. So the vertex is (0,3).

What does it mean when b = 0 in a quadratic?

When b = 0, there's no x-term in the equation. This means the parabola is perfectly centered on the y-axis, so the vertex always has x-coordinate = 0.

How do I remember the vertex formula?

Think of it as "negative b over 2a": $x = -\frac{b}{2a}$ . The negative sign is crucial - don't forget it!

Is this parabola opening up or down?

Since a = 1 > 0, this parabola opens upward. The vertex (0,3) is the lowest point on the graph.

What if I get confused about which coordinate is which?

Remember: (x, y) means "across, then up". The first number is how far left or right, the second is how far up or down from the origin.

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Pinpoint the Vertex of the Quadratic Function: y = x² + 3

Vertex Form with Constant Terms

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the vertex at (0,3) and not (3,0)?

What does it mean when b = 0 in a quadratic?

How do I remember the vertex formula?

Is this parabola opening up or down?

What if I get confused about which coordinate is which?

🌟 Unlock Your Math Potential

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