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

Answer:

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

Step-by-step 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

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

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

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

$\implies x-1=\pm \sqrt{36}$

$\implies x=1\pm 6$

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

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