Question

Which equation is represented by the graph?

A:
y= (£-1)+3
B:
4=(¢- 32+1
C:
9=-¢+32_1
D:
4=-¢- 32+1

Answer 1

C: y = -(x +3)² -1

Explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

Vertex form

For vertex (h, k), the vertex form equation of a parabola is ...

y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

y = a(x -(-3))² + (-1)

y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

y = -(x +3)² -1

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Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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