Answer:
Step-by-step explanation:
The directrix of the parabola is the horizontal line with the eqaution The focus of the parabola is at point (-4,10), than the axis of symmetry of the parabola is the perpendicular line to the directrix passing through the focus. Its equation is
The distance between the directrix and the focus is so
and the vertex is at point
Parabola goes in positive y-direction, hence its equation is
where is the vertex, so the equation of this parabola is
Answer:
A hole at x=-4.
Step-by-step explanation:
This is a fraction so we have to worry about division by zero.
The only time we will be dividing by 0 is when x+4 is 0.
Solving the equation
x+4=0 for x:
Subtract 4 on both sides:
x=-4
So there is either a vertical asymptote or a hole at x=-4.
These are the kinds of discontinuities we can have for a rational function.
If there is a hole at x=-4, then x=-4 will make the top zero and can be cancelled out after simplification.
If is is a vertical asymptote, x=-4 will make the top NOT zero.
Let's see what -4 for x in x^2+6x+8 gives us:
(-4)^2+6(-4)+8
16+-24+8
-8+8
0
Top and bottom are 0 when x=-4.
Let's see what happens after simplication.
We are going to factor a^2+bx+c if factorable by finding two numbers that multiply to be c and add up to be b.
So what 2 numbers together multiply to be 8 and add up to be 6.
I hoped you said 4 and 2 because (4)(2)=8 where 4+2=6.
We we able to cancel out that factor that was giving us x=-4 is a zero.
Therefore there is a hole at x=-4.