Use the functions f(x) = 2x2 + 3 and g(x) = 3x + 5 to evaluate the composite function. f(g(3))
1 answer:
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Answer:
Part A)
The <em>x-</em>intercepts are (-1/4, 0) and (4, 0).
Part B)
The vertex is a maximum because the leading coefficient is negative.
The vertex is (1.875, 72.25).
Part C)
We can plot the zeros and the vertex, and connect them with a curve.
Step-by-step explanation:
The function given is:
Part A)
To find the <em>x-</em>intercepts of the function, set the function equal to 0 and solve for <em>x: </em>
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We can divide both sides by negative four:
Factor:
Zero Product Property:
Solve for each case:
Hence, our zeros are:
Part B)
Note that the leading coefficient of our function is negative.
So, our function will be concave down.
Hence, our vertex will be the maximum.
The vertex is given by:
In this case, <em>a </em>= -16, <em>b</em> = 60, and <em>c</em> = 16.
Find the <em>x-</em>coordinate of the vertex:
Substitute this back into the function to find the <em>y-</em>coordinate:
Hence, our vertex is:
Part C)
Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.
The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the <em>y-</em>intercept.
Answer:
The answer to the question is
37.5 ft² of fabric is needed to make the parallelogram pieces for 24 blocks.
Step-by-step explanation:
To answer the question, we note that a parallelogram is a four sided polygon having two opposite parallel sides.
Therefore in this question, we select our parallelogram to be a rectangle
Number of pieces of parallelogram in a quilted block = 8
Number of parallelogram in each quadrant of the quilted block = 2
Therefore the height of the rectangle = 2 × the base = 2× = 7.5 inches
Therefore the area of each parallelogram = base × height
= =
in²
since each quilted block uses 8 parallelogram, then the amount of fabric for each quilted block is
Hence 24 blocks wil require 24×225 in² = 5400 in²
However, since 144 in² = 1 ft² we have
5400 in² = 5400 in²× 1/144 ft²/in² = 37.5 ft².