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

To find the vertex of the quadratic function \( y = 4x^{2} + 3x - 8 \), we can use the vertex formula \( x = -\frac{b}{2a} \). Here, \( a = 4 \) and \( b = 3 \). Substituting these values gives us \( x = -\frac{3}{2 \cdot 4} = -\frac{3}{8} \). Plugging this value of \( x \) back into the equation yields the vertex's y-coordinate. The vertex can be represented as the point where the parabola reaches its maximum or minimum value. For this quadratic, since the coefficient of \( x^2 \) (which is 4) is positive, the parabola opens upwards. Thus, the vertex represents the minimum point of the graph. You can plug in various x-values to confirm the shape of the parabola and get a better idea of its behavior. In addition to finding the vertex, it's essential to understand where the graph intersects the x-axis, which will help you sketch it accurately. The quadratic formula can help you find these x-intercepts, giving you a more complete picture of the graph's behavior.