We want to identify different things on the given graph.
The solutions are:
A) (3, -1)
B) x = 4
C) x = y^2 + 2y + 4
D) x ⇒ ∞, y ⇒ ∞
x⇒3, y⇒ -1
A) The first thing we want to identify is the vertex, we could say that a vertex is a point of symmetry. (like the minimum/maximum of a parabola). Here we clearly do not have a point of symmetry, as we only have half of a parabola, but if it was a complete one, the vertex would be at the blue point, in (3, -1)
B) This is the point where the graph intercepts the x-axis, x = 4.
C) we want to write the equation, we start with the general parabola, this time as a function of y:
x = a*y^2 + b*y + c
Remember that the x-itercept is at x = 4. then c = 4.
x = a*y^2 + b*y + 4
The y-value of the vertex is -1, while the general y-value of the vertex is:
y = -b/2a = -1
And evaluating the equation in this value, gives us:
x = a*(-1)^2 + b*-1 + 4 = 3
Then we have two equations:
-b/2a = -1
a + -b + 4 = 3
We can rewrite the first one as:
-b = -2a
b = 2a
Now we can replace this on the other equation:
a - 2a + 4 =3
-a + 4 = 3
-a = 3 - 4 = -1
a = 1
And b = 2a = 2*1 = 2
Then the equation of the parabola is:
x = y^2 + 2y + 4
D) We can see that as x grows, y increases, so we can say that:
x ⇒ ∞, y ⇒ ∞
And for the other limit we can see that as x tends to 3, y tends to -1, then:
x⇒3, y⇒ -1
If you want to learn more, you can read:
brainly.com/question/21685473
