The equation \(y=2x^2+0.5x-4\) is graphed.

Based on the graph, what number could you put in the box to create an equation that has no real solutions?
\(\displaystyle 2x^2+0.5x-4 = \boxed{\phantom{30}}\)

The equation \(y = 1.5x^2-3x+2\) is graphed.

1. Without calculating the solutions, determine whether \(1.5x^2-3x+2=0\) has real solutions.
2. Show how to solve \(1.5x^2-3x+2=0\).

Write a quadratic equation of the form \(ax^2 + bx + c = 0\) with real coefficients that has two non-real solutions. How did you decide what equation to write?

Find the complex solutions to each equation.

1. \(\text-2x^2+2x=2.5\)
2. \(4.5x^2+3x+\frac12=0\)
3. \(\frac12 x^2+5x=\text-14\)
4. \(\text- x^2 -1.5x + 5 = 7\)

Elena and Kiran solve the equation \(2x^2-4x+3=0\) and they get different answers. Elena writes \(1 \pm i\sqrt{0.5}\), and Kiran writes \(1 \pm \frac{i\sqrt8}{4}\). Are their answers equivalent? Say how you know.