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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.​

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Semsee45idn

Answer:

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

Step-by-step explanation:

Vertex form

[tex]y=a(x-h)^2+k[/tex]  

(where (h, k) is the vertex)

Given:

  • vertex = (1, -108)

[tex]\implies y=a(x-1)^2-108[/tex]

Given:

  • y-intercept = (0, -105)

[tex]\implies a(0-1)^2-108=-105[/tex]

[tex]\implies a(-1)^2=-105+108[/tex]

[tex]\implies a=3[/tex]

Therefore:

[tex]\implies y=3(x-1)^2-108[/tex]

The x-intercepts are when y = 0

[tex]\implies 3(x-1)^2-108=0[/tex]

[tex]\implies 3(x-1)^2=108[/tex]

[tex]\implies (x-1)^2=36[/tex]

[tex]\implies x-1=\pm \sqrt{36}[/tex]

[tex]\implies x=1\pm 6[/tex]

[tex]\implies x=7, x=-5[/tex]

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

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