Answer:
y = -1/10x^2 +2.5
Step-by-step explanation:
The distance from focus to directrix is twice the distance from focus to vertex. The focus-directrix distance is the difference in y-values:
-1 -4 = -5
So, the distance from focus to vertex is p = -5/2 = -2.5. This places the focus 2.5 units below the vertex. Then the vertex is at (h, k) = (0, -1) +(0, 2.5) = (0, 1.5).
The scale factor of the parabola is 1/(4p) = 1/(4(-2.5)) = -1/10. Then the equation of the parabola is ...
y = (1/(4p))(x -h) +k
y = -1/10x^2 +2.5
_____
You can check the graph by making sure the focus and directrix are the same distance from the parabola everywhere. Of course, if the vertex is halfway between focus and directrix, the distances are the same there. Another point that is usually easy to check is the point on the parabola that is even with the focus. It should be as far from the focus as it is from the directrix. In this parabola, the focus is 5 units from the directrix, and we see the points on the parabola at y=-1 are 5 units from the focus.
Answer:
a) response variable
Step-by-step explanation:
The response variable is the variable that depends on other variables such as the independent or explanatory variable, it is the variable that is being tested. The response variable is also called the dependent variable.
In linear regression, the y variable is referred to as the response variable while the x variable is referred to as the explanatory or independent variable.
In this case the y variable is "the number of times they cough in a day" and this variation depends on the x variable "number of cigarettes a person smokes in a day".
Answer:
73
Step-by-step explanation:
you write 12 instead of b
So by looking at this equation you should look to see it's key features which will help you graph the equation. the first key feature is the slope, the slope lets you know the angle at which the line will be, the slope in an equation will always be the number multiplied by x ( in this case it'd be 3/4). The second feature is the y intercept, the y intercept is where the equations line crosses the y axis, the y intercept in a graph will always be what is added or subtracted after the x (in this case it'd be 3).
To simplify what I said look at the following:
Slope: 3/4
Y intercept: 3
Hope this helps!
