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The quadratic function given by:
is in vertex form. The graph of is a parabola whose axis is the vertical line
and whose vertex is the point
. So:
To translate the graph of a function to the right, left, upward or downward we have:
By knowing this things, we can solve our problem as follows:
FIRST.
- Translating <em>11 units to the left:</em>
- Then translating<em> 5 units down:</em>
Since the new function is fatter, the factor we need to multiply the term <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.
<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>
SECOND.
- Translating <em>8 units to the right:</em>
- Then translating<em> 1 unit down:</em>
As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.
<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>
Hey there,
So, we need to remember that the circumference of a circle is
3.14
So this means that we would do 500×3.14.
And by this we do. .
Firstly, work out 4 × 500. As mentioned before, we can ignore the decimal point for now. The smaller figures in green are the tens figures carried over. Working from right to left:
4 × 0 = 0
4 × 0 = 0
4 × 5 = 20
<span>Put the 0 in the appropriate column and carry the 2.
</span>
We now work out 10 × 500.
This can be written as 1 × 500 × 10.
Because we are multiplying by 10, we place 1 zero to the right and then work out 1 × 500.
1 × 0 = 0
1 × 0 = 0
<span>1 × 5 = 5
</span>
Lastly, work out 300 × 500.
This can be written as 3 × 500 × 100.
Because we are multiplying by 100, we place 2 zeroes to the right and then work out 3 × 500.
3 × 0 = 0
3 × 0 = 0
3 × 5 = 15
<span>
Put the 5 in the appropriate column and carry the 1
</span>Finally the 3 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.
0 + 0 + 0 = 0
0 + 0 + 0 = 0
0 + 0 + 0 = 0
0 + 5 + 2 = 7
5 = 5
1 = 1
How is the decimal point positioned? 3.14 has 2 digits after the decimal point.
The final answer must also have 2 digits after the decimal point.
<span>So: 500 × 3.14 = </span>
~Jurgen
So, we need to remember that the circumference of a circle is
So this means that we would do 500×3.14.
And by this we do. .
Firstly, work out 4 × 500. As mentioned before, we can ignore the decimal point for now. The smaller figures in green are the tens figures carried over. Working from right to left:
4 × 0 = 0
4 × 0 = 0
4 × 5 = 20
<span>Put the 0 in the appropriate column and carry the 2.
</span>
We now work out 10 × 500.
This can be written as 1 × 500 × 10.
Because we are multiplying by 10, we place 1 zero to the right and then work out 1 × 500.
1 × 0 = 0
1 × 0 = 0
<span>1 × 5 = 5
</span>
Lastly, work out 300 × 500.
This can be written as 3 × 500 × 100.
Because we are multiplying by 100, we place 2 zeroes to the right and then work out 3 × 500.
3 × 0 = 0
3 × 0 = 0
3 × 5 = 15
<span>
Put the 5 in the appropriate column and carry the 1
</span>Finally the 3 rows are added together starting at the right. The smaller figures in green are the tens figures carried over.
0 + 0 + 0 = 0
0 + 0 + 0 = 0
0 + 0 + 0 = 0
0 + 5 + 2 = 7
5 = 5
1 = 1
How is the decimal point positioned? 3.14 has 2 digits after the decimal point.
The final answer must also have 2 digits after the decimal point.
<span>So: 500 × 3.14 = </span>
~Jurgen