Consider the graph of the quadratic function y=-2(x + 2)2
- 1 with no real zeros.
What number can be added to the right side of the
equation to change it to a function with one real root?
6 5 4 3 ² 1
2
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-3-

1

Step-by-step explanation:

The quadratic function

y = -2(x + 2)²  - 1

has no real zeros because its vertex is located at (-2, -1) and it opens downward (the leading coefficient, -2, is negative)

A quadratic function has one real root if its vertex has the form (x, 0). If we add 1 to our equation, we get:

y = -2(x + 2)²  - 1 + 1 = -2(x + 2)²

which has point (-2, 0) as vertex

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