To find the vertex of the quadratic function \( y = 4x^2 + 3x - 8 \), we can use the vertex formula. The vertex \( (h, k) \) of a quadratic function in the form \( y = ax^2 + bx + c \) can be found using:
\[ h = -\frac{b}{2a} \]
where \( a = 4 \) and \( b = 3 \).
- Calculate \( h \):
\[ h = -\frac{3}{2 \times 4} = -\frac{3}{8} = -0.375 \]
- Next, substitute \( h \) back into the equation to find \( k \):
\[ k = 4(-0.375)^2 + 3(-0.375) - 8 \]
Calculating \( k \):
\[ k = 4(0.140625) - 1.125 - 8 \] \[ k = 0.5625 - 1.125 - 8 \] \[ k = 0.5625 - 9.125 = -8.5625 \]
Thus, the vertex of the quadratic \( y = 4x^2 + 3x - 8 \) is approximately:
\[ (-0.375, -8.5625) \]
Now, looking at the provided options, selection C is the closest match:
C. \( (-0.375, -8.563) \)
Therefore, the vertex of the quadratic is:
C. (-0.375, -8.563)