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

Guest Oct 30, 2022

#2**0 **

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

–y^{2} + 4y – 4 – 2y + 7

combine terms to get –y^{2} + 2y + 3 set this equal to zero –y^{2} + 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 y^{2}) y^{2} – 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**

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Guest Oct 30, 2022