Question

100 POINTS

7. Which equation has a graph that is a parabola with a vertex at (1, –1)? y = (x – 1)2 + 1 y = (x – 1)2 – 1 y = (x + 1)2 + 1 y = (x + 1)2 – 1

Answer 1

`\sf y = (x - 1)^2 - 1`

Explanation:

The equation of a parabola with a vertex at (h, k) is:

`\sf y = a(x - h)^2 + k`

where a is a constant that determines the shape of the parabola.

If we substitute (h, k) = (1, -1) into this equation, we get:

`\sf y = a(x - 1)^2 - 1`

The only equation of the given choices that matches this form is:

`\sf y = (x - 1)^2 - 1`

Therefore, the equation that has a graph that is a parabola with a vertex at (1, -1) is:

`\sf y = (x - 1)^2 - 1`