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:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is :
1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.
So, substituting x = 0 in the equation, we get
So, the diving board is 6 feet above the surface of the water.
2. From the equation, we known that it is a parabola and the vertex is minimum.
It is the minimum height which represents the depth Kendra dives into the water.
So the coordinate of the vertex is =
Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,
a = 1 and b = -7
∴ x coordinate =
Now substituting to find f(x),
= -6.25
Therefore, the diver dives 6.25 feet below the water surface.
3. The horizontal distance from the board the diver enters into the water.
This is the y-intercept and it is the value of x when h(x)=0.
∴
Factorizing, we get
∴
So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.
4. We know that the equation given has x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height
. The height is the water surface level.
The first x intercept represents the points where Kendra dives into the water.
And the second x intercept is the point where Kendra comes out of the water surface. This this is for
.
Thus Kendra dives out of the water surface at 6 feet from the board.
