What is the vertex of the function?

f(x)=4x2+8x+3

To find the vertex of a quadratic function of the form \( f(x) = ax^2 + bx + c \), we use the vertex formula:

\[
x = \frac{-b}{2a}
\]

For the given function \( f(x) = 4x^2 + 8x + 3 \), we have:
- \( a = 4 \)
- \( b = 8 \)

Let's calculate the \( x \)-coordinate of the vertex:

\[
x = \frac{-8}{2(4)} = \frac{-8}{8} = -1
\]

Now, substitute \( x = -1 \) back into the function to find the \( y \)-coordinate:

\[
f(-1) = 4(-1)^2 + 8(-1) + 3 = 4(1) - 8 + 3 = 4 - 8 + 3 = -1
\]

So, the vertex is \( (-1, -1) \).

### The vertex of the function is \( (-1, -1) \).

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:
1. How do you find the axis of symmetry for a quadratic function?
2. What is the significance of the vertex in a quadratic function?
3. How does the coefficient of \( a \) affect the direction of the parabola?
4. Can you rewrite the quadratic function in vertex form?
5. How do you find the intercepts of a quadratic function?

**Tip:** The vertex form of a quadratic function, \( f(x) = a(x-h)^2 + k \), makes it easier to identify the vertex and graph the function.

What is the vertex of the function f(x) = 4x^2 + 8x + 3?

Discover how to find the vertex of the quadratic function f(x) = 4x^2 + 8x + 3 using the vertex formula. This step-by-step solution demonstrates key algebraic concepts for students in Grades 9-11.

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