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timama [110]
3 years ago
13

The graph shows the relationship between the height of a tree and its age in years. What is the unit rate of growth for the tree

?
A. 0.25 feet per year
B. 0.5 feet per year
C. 2 feet per year
D. 3 feet per year

Mathematics
2 answers:
vaieri [72.5K]3 years ago
5 0

Answer:

Option (c) is corrrect.

The unit rate of growth for the tree is 2 feet per year.

Step-by-step explanation:

Given : A graph showing the relationship between the height of a tree and its age in years.

We have to find the unit rate of growth for the tree.

Consider the given graph.

Since, the slope of the graph gives the rate of change occurring per year.

Here, The slope will give the unit rate of growth for the tree.

Consider two points on the equation of line,

(1,2) and (2,4)

Slope between two points is given by ,

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(1,\:2\right),\:\left(x_2,\:y_2\right)=\left(2,\:4\right)

Subsitute, we have,

m=\frac{4-2}{2-1}=2

Thus, The unit rate of growth for the tree is 2 feet per year.

adoni [48]3 years ago
3 0
C. 2 feet per year
Hope this helps!
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(x - 3)2 - 2 = 0.

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To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

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Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

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