Question

What is the equation of the following graph in vertex form?

Courtesy of Texas Instruments (2 points)


y = (x - 3)2 - 1

y = (x + 3)2 - 1

y = (x - 4)2 - 2

y = (x - 4)2 + 8

Answer 1

y = (x + 3)2 - 1

Explanation:

Answer 2

For this case we have:

The equation in vertex form of the parabola is given by:

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

The vertex is (h, k) and is given by the highest or lowest point of the parabola, in this case it is observed that it is
`(h, k) = (- 3, -1)\\`

Thus, the equation is given by:

`y = a (x - (- 3)) ^ 2 + (- 1)\\\\y = a (x + 3) ^ 2-1\\`

We look for the value of a, substituting a point of the parabola in the equation in the form of vertex, we will take the point
`(x, y) = (0,8)\\`

Substituting we have:

`8 = a (0 - (- 3)) ^ 2 + (- 1)\\\\8 = a (0 + 3) ^ 2-1\\\\8 = a (3) ^ 2-1\\`

`8 = 9a-1\\\\8 + 1 = 9a\\\\9 = 9a\\`

`a = (9)/(9)\\\\a = 1\\`

Thus, the equation of the parabola is given by:

`y = (x + 3) ^ 2-1\\`

Answer:

`y = (x + 3) ^ 2-1`