To find the vertex of the quadratic function \( y = 4x^2 + 3x - 8 \), we can use the vertex formula. The x-coordinate of the vertex for a quadratic function in the form \( ax^2 + bx + c \) is given by:
\[ x = -\frac{b}{2a} \]
In this case, \( a = 4 \) and \( b = 3 \).
Substituting these values into the formula:
\[ x = -\frac{3}{2 \cdot 4} = -\frac{3}{8} = -0.375 \]
Next, we find the y-coordinate of the vertex by substituting \( x \) back into the original equation:
\[ y = 4(-0.375)^2 + 3(-0.375) - 8 \]
Calculating \( (-0.375)^2 \):
\[ (-0.375)^2 = 0.140625 \]
Now substitute back:
\[ y = 4(0.140625) + 3(-0.375) - 8 \] \[ y = 0.5625 - 1.125 - 8 \] \[ y = 0.5625 - 9.125 \] \[ y \approx -8.5625 \]
Thus, the vertex is approximately \( (-0.375, -8.563) \).
So, the correct response is:
\[ \text{(−0.375,−8.563)} \]