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