+0  
 
0
28
2
avatar

How many y-intercepts does the graph of the parabola x = -y^2 + 4y - 4 - 2y + 7 have?

 Oct 30, 2022
 #1
avatar
0

There are 0 intercepts.

 Oct 30, 2022
 #2
avatar
0

 

How many y-intercepts does the graph of the parabola x = -y^2 + 4y - 4 - 2y + 7 have?  

 

–y2 + 4y – 4 – 2y + 7  

 

combine terms to get –y2 + 2y + 3    set this equal to zero     –y2 + 2y + 3 = 0  

 

Multiply both sides by –1  

You don't have to do this, but I find it easier when the   

highest order term is positive (in this case, the y2)                  y2 – 2y – 3 = 0  

 

Looking at the quadratic, we see it can be factored                 (y – 3)(y + 1) = 0  

 

Knowing that the curve crosses the y-axis when x = 0  

set each factor equal to zero and the intercepts are at             y = +3  and  y= –1  

 

The problem asked for how many, so the answer is  2  

.

 Oct 30, 2022

28 Online Users

avatar