+0

# Parabola

0
37
2

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

Jun 21, 2022

#2
+2339
+1

Set $$x = 0$$ and simplify the equation: $$0 = -y^2 + 2y + 3$$

We can solve for the number of solutions with the discriminant($$b^2 - 4ac$$)

Note that the discriminant is $$2^2 - 4 \times 3 \times -1 = 16$$. Because the discriminant is positive, it will have exactly $$\color{brown}\boxed{2}$$ y-intercepts.

Jun 21, 2022

#1
0

The graph has one intercept.

Jun 21, 2022
#2
+2339
+1

Set $$x = 0$$ and simplify the equation: $$0 = -y^2 + 2y + 3$$

We can solve for the number of solutions with the discriminant($$b^2 - 4ac$$)

Note that the discriminant is $$2^2 - 4 \times 3 \times -1 = 16$$. Because the discriminant is positive, it will have exactly $$\color{brown}\boxed{2}$$ y-intercepts.

BuilderBoi Jun 21, 2022