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Sagot :
Answer:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is : [tex]$h(x)=x^2-7x+6$[/tex]
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
[tex]$h(0)=0^2-7(0)+6$[/tex]
[tex]$=0-0+6$[/tex]
[tex]$=6$[/tex]
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 [tex]$x$[/tex] coordinate of the vertex is = [tex]$\frac{-b}{2a}$[/tex]
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 = [tex]$\frac{-(-7)}{2 \times 1} $[/tex]
[tex]$\frac{7}{2}=3.5$[/tex]
Now substituting to find f(x),
[tex]$h(3.5)=(3.5)^2-7(3.5)+6$[/tex]
= -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.
∴ [tex]$0=x^2-7x+6$[/tex]
Factorizing, we get [tex]$(x-1)(x-6)=0$[/tex]
∴ [tex]$x=1 \text{ or}\ x=6$[/tex]
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 [tex]$\text{two}$[/tex] x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height [tex]$h(x)=0$[/tex]. 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 [tex]$x=6$[/tex] for [tex]$h(x)=0$[/tex].
Thus Kendra dives out of the water surface at 6 feet from the board.
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