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 equation in the form \( y = ax^2 + bx + c \) is given by the formula:
\[ x = -\frac{b}{2a} \]
In this equation, \( a = 4 \) and \( b = 3 \). Plugging in these values:
\[ x = -\frac{3}{2(4)} = -\frac{3}{8} \approx -0.375 \]
Now, we need to find the y-coordinate of the vertex by substituting \( x = -0.375 \) back into the original quadratic equation:
\[ y = 4(-0.375)^2 + 3(-0.375) - 8 \]
Calculating step by step:
- \( (-0.375)^2 = 0.140625 \)
- \( 4 \times 0.140625 = 0.5625 \)
- \( 3 \times (-0.375) = -1.125 \)
- Now substitute these values into the equation: \[ y = 0.5625 - 1.125 - 8 = 0.5625 - 1.125 - 8 = -8.5625 \]
Thus, the vertex of the quadratic \( y = 4x^2 + 3x - 8 \) is approximately:
\[ (-0.375, -8.563) \]
So the answer is:
(−0.375,−8.563)