Question

Find the x-intercepts of the parabola with vertex (1,-108) and y-intercept (0,-105). Write your answer in this form: (X1,y1), (x2,y2). If necessary, round to the nearest hundredth.​

Answer 1

(7, 0) and (-5, 0)

Explanation:

Vertex form

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

(where (h, k) is the vertex)

Given:

• vertex = (1, -108)

`\implies y=a(x-1)^2-108`

Given:

• y-intercept = (0, -105)

`\implies a(0-1)^2-108=-105`

`\implies a(-1)^2=-105+108`

`\implies a=3`

Therefore:

`\implies y=3(x-1)^2-108`

The x-intercepts are when y = 0

`\implies 3(x-1)^2-108=0`

`\implies 3(x-1)^2=108`

`\implies (x-1)^2=36`

`\implies x-1=\pm √(36)`

`\implies x=1\pm 6`

`\implies x=7, x=-5`

Therefore, the x-intercepts are (7, 0) and (-5, 0)