What is the vertex of the quadratic function y = 2(x - 3)²   + 4 ?*

10 points

(3,4)

(-3,4)

(3,-4)

(-3,-4)

The vertex form of a quadratic function is generally written as:

\[
y = a(x - h)^2 + k
\]

where \((h, k)\) is the vertex of the parabola.

Given the function:

\[
y = 2(x - 3)^2 + 4
\]

- \(h = 3\)
- \(k = 4\)

Thus, the vertex is:

\[
(3, 4)
\]

So, the correct answer is **(3, 4)**.

Would you like to see further details or have any questions?

Here are 5 related questions:

1. What is the axis of symmetry for the function \( y = 2(x - 3)^2 + 4 \)?
2. How do you find the x-intercepts of a quadratic function?
3. What is the effect of changing the value of \( a \) in the vertex form of a quadratic function?
4. How would the graph of the function change if the equation was \( y = 2(x + 3)^2 + 4 \)?
5. How do you find the y-intercept of a quadratic function in vertex form?

**Tip:** The sign of \( h \) in the vertex form \( y = a(x - h)^2 + k \) is always opposite when determining the vertex.

Learn how to find the vertex of the quadratic function y = 2(x - 3)^2 + 4. This problem involves identifying the vertex form of a quadratic equation and determining the vertex coordinates. Suitable for students in Grades 10-12.

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