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.