Transformations

Question

Which of the following are possible equations of a parabola that has no real solutions and opens downward?

y > = -(x + 4)² - 2

y > = -(x + 4)² + 2

y > = -x² - 2

y > = (x - 4)² + 2

y > = -(x - 4)² - 2

Answer 1

You want the vertex to be below the origin

that means either the 1st, last or middle equations which have y intercept =-2

to be downward opening, the coefficient of the x^2 term must be negative

the 1st, 3rd and 5th are all downward opening with no real solution. They are parabolas that never intersect the x axis, so they have no real zeros, no real solutions, just imaginary solutions.