Graph the quadratic $$ y=4 x^{2}+3 x-8 $$. What is the vertex of this quadratic? (f point) $$ (0,-8) $$ $$ (-1.838,0) $$ $$ (1.088,0) $$ $$ (-0.375,-8.563) $$

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To find the vertex of the quadratic function $$ y = 4x^{2} + 3x - 8 $$, we'll use the vertex formula for a parabola.

### Step 1: Identify the coefficients
The general form of a quadratic equation is:
$$ y = ax^{2} + bx + c $$
For the given equation:
- $$ a = 4 $$
- $$ b = 3 $$
- $$ c = -8 $$

### Step 2: Find the x-coordinate of the vertex
The x-coordinate of the vertex ($$ h $$) can be found using:
$$ h = -\frac{b}{2a} $$
Plugging in the values:
$$ h = -\frac{3}{2 \times 4} = -\frac{3}{8} = -0.375 $$

### Step 3: Find the y-coordinate of the vertex
Substitute $$ x = -0.375 $$ back into the original equation to find the y-coordinate ($$ k $$):
$$
\begin{align*}
y &= 4(-0.375)^{2} + 3(-0.375) - 8 \
&= 4(0.140625) - 1.125 - 8 \
&= 0.5625 - 1.125 - 8 \
&= -8.5625
\end{align*}
$$
Rounding to three decimal places:
$$ k \approx -8.563 $$

### Conclusion
The vertex of the quadratic function $$ y = 4x^{2} + 3x - 8 $$ is:
$$ \boxed{\,(-0.375,\ -8.563)\,} $$
The vertex of the quadratic $$ y = 4x^{2} + 3x - 8 $$ is at $$ (-0.375, -8.563) $$.

Graph the quadratic . What is the vertex of this quadratic? (f point)

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