To find the vertex of the quadratic function \( y = 2x^2 - 4.5x + 2 \), we can use the vertex formula. The \(x\)-coordinate of the vertex for a quadratic in the form \( y = ax^2 + bx + c \) is given by:
\[ x = -\frac{b}{2a} \]
In this case, \( a = 2 \) and \( b = -4.5 \). Plugging in the values:
\[ x = -\frac{-4.5}{2 \cdot 2} = \frac{4.5}{4} = 1.125 \]
Next, we substitute \( x = 1.125 \) back into the original equation to find the \(y\)-coordinate of the vertex:
\[ y = 2(1.125)^2 - 4.5(1.125) + 2 \]
Calculating \( (1.125)^2 \):
\[ (1.125)^2 = 1.265625 \]
Now substituting into \(y\):
\[ y = 2(1.265625) - 4.5(1.125) + 2 \]
Calculating \( 2(1.265625) \):
\[ 2(1.265625) = 2.53125 \]
Calculating \( -4.5(1.125) \):
\[ -4.5(1.125) = -5.0625 \]
Putting it all together:
\[ y = 2.53125 - 5.0625 + 2 = 2.53125 - 5.0625 + 2 = -0.53125 \]
Therefore, the coordinates of the vertex of the parabola are:
\[ (1.125, -0.53125) \]
This is closest to the response \( (1.125, -0.531) \).
The correct answer is:
(1.125, -0.531)