Question
Asked Dec 12, 2019
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Given the parabola f(x)= x2-2x-3 complete parts (1) through (3) below. 

  1. Find the vertex by averaging the x-intercepts.

  2. Find the vertex by completing the square.

  3. Find the vertex of f(x)= x2+5x+2 using your method of choice.

  4. What are the domain and range for f(x)=x2+5x+2?

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Expert Answer

Step 1
  1. Obtain the vertex by averaging the x-intercept.

Equate f (x) to 0 and obtain the x-intercepts.

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f(x)= 0 x - 2x – 3 = 0 (x – 3)(x+1)=0 x = 3,-1 Then x-intercepts are (3,0) and (-1,0).

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Step 2

Consider p = 3 and q = –1 and the vertex can be obtaining by axis of symmetry.

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p+q_ 3-1 2 =1 3 -1 2 p+q p+q Vertex =(1.f(1)) )| (1, –4)

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Step 3
  1. Find the vertex by completing the ...
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The general equation of a parbola is y =(x-a)' +b Where (a,b) is the vertex of the parabola. y =x² – 2x – 3 y =x – 2x +-3+1-1 [:: Add and subtract 1] y = (x² – 2r +1)–1-3 y=(x-1) -4 2.x By comparing the above equation with genearl form, the vertex is (1,–4)|

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