How do you interpret slope and y- intercept from a table?
1 answer:
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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.
Answer:
x = 2√2
y = 2√6
Step-by-step explanation:
Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)
These will be equal since the triangles are similar
shorter leg : longer leg
(blue triangle = red triangle)
⇒ x : 4 = 2 : x
⇒ x/4 = 2/x
⇒ x² = 8
⇒ x = √8
⇒ x = 2√2
Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.
Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)
⇒ 4² + (2√2)² = y²
⇒ y² = 24
⇒ y = √24
⇒ y = 2√6
