Questions – Impulse and Momentum
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The equation of the vertical parabola in vertex form is written as
Where (h, k) are the coordinates of the vertex and p is the focal distance.
The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.
Using this value for p and (3, 1) as the vertex, we have our equation
End behavior of a polynomial function is based on the <u>degree of the function</u> and the <u>sign of the leading coefficient</u>.
<u>Sign of the Leading Coefficient</u> determines behavior of right side:
- Positive: right side goes to positive infinity
- Negative: right side goes to negative infinity
<u>Degree of the function</u> determines the behavior of the left side:
- Odd degree: left side is opposite direction of right side
- Even degree: left side is same direction as right side
If you have an expression in the denominator, then you must divide the denominator into the numerator. The result will have a degree and a leading coefficient. Use the rules stated above to determine the end behavior.
For example:
y =
We can factor to get: y =
y = x + 3
Leading Coefficient of y = x + 3 is positive so right side goes to positive infinity.
Degree of y = x + 3 is odd so left side is opposite direction of right side, which means left side goes to negative infinity.
The denominator may not divide evenly into the numerator thus leaving a remainder, but that is ok. We can still use the rules stated above.