Phyllis has a problem. She knows that the roots of a quadratic function are
Mercedes says, “Just remember when we made factors from the roots. If the roots are
and the equation is .” Use Mercedes’s idea to help Phyllis write the equation of a quadratic function.
Generic rectangle, 2 rows, 2 columns, top edge labeled, x minus quantity, 3 + 4 I, left edge labeled, x, minus quantity, 3 minus 4 i.
Labels added: Interior, top left, x squared, to right, negative x times the quantity, 3 + 4 I, bottom left, negative x times the quantity, 3 minus 4 I, bottom right, quantity, 3 minus 4 I, times the quantity, 3 + 4 I.
Interior labels changed: top left, negative 3 x, minus 4 x I, bottom left, negative 3 x, + 4 x I, bottom right, 25.
Darin says, “No, no, no. You can do it that way, but that’s too complicated. I think you just start with
and work backwards. So , then, square both sides… Yeah, that’ll work.” Try Darin’s method.
Whose method do you think Phyllis should use? Explain your choice.