College Alebra Question PLEASE SHOW ALL WORK do NOT skip or

College Alebra Question. PLEASE SHOW ALL WORK (do NOT skip or combine any steps). I know the answer but I don\'t know how they arrived at that answer.

9. Choose the equation that yields the given graph. uation that yields the given grmph 2 ANSWER: y (x-1)2-1

Solution

From the graph, it is clear that the graph is a Parabola.

The general equation for parabola is y=a(x-h)²+k

where a is constant

(h,k) is Vertex of parabola

Vertex is the lowest point in the graph or bottem point of U-shape.

From the graph,Vertex(h,k) = (1,-1)

A point on the graph(x,y) is (2,0)

Substitute (x,y) and (h,k) in the general equation form y=a(x-h)²+k to find \'a\'

y=a(x-h)²+k

0=a(2-1)²+(-1)

0=a(1)²-1

0=a(1)-1

a-1=0

a=1

Substitute Vertex and constant in the general equation form y=a(x-h)²+k

y=1(x-1)²+(-1)

y=(x-1)²-1

Therefore,the equation of the graph is y=(x-1)²-1