A parabola has its vertex at (2, 1) and crosses x-axis at (1, 0) and at (3, 0). Which of the follwoing equations below has this parabola for its graph?

Question

A. y= 1 - (x-2)2 (that's supposed to be to the second power)

B. y= 1 + (x+2)2 (to the second power)

C. y= -1 - (x+2)2 (to the second power)

D. y= -1 - (x-2)2 (to the second power)

Answer 1

Start with y = a(x-h)² + k

 

The vertex is (h,k) = (2,1) so we plug this in to get

 

y = a(x-2)² + 1

 

Now plug in one of the x-intercepts, say (1,0)

 

a(1-2)² + 1 =0

 

(-1)²a = -1

 

a = -1

 

So it is

 

y = 1 - (x - 2)²

 

which is choice A.