How do you graph -0.5x2 2x 1?

To graph the quadratic function ( y = -0.5x^2 + 2x + 1 ), first identify the vertex, which can be found using the formula ( x = -\frac{b}{2a} ). For this equation, ( a = -0.5 ) and ( b = 2 ), so the vertex occurs at ( x = 2 ). Calculate the corresponding ( y ) value to find the vertex point, and then plot additional points by substituting values for ( x ) into the equation. Finally, draw a smooth curve to represent the parabola, which opens downwards due to the negative coefficient of ( x^2 ).