Does this graph represent a function? Why or why not?
1 answer:
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<span>The definition of quadratic function is given by:
</span>
<span>
So the problem asks for two conditions:
<em>1. Write the quadratic function in factored form. </em>
<em>2. The vertex has an x-coordinate of 3.</em>
Then the equation (1) must be written as follows:
</span>
<span>
To satisfy the two conditions:
So we are free to choose the value of one root, say:
Thus:
Finally, the answer is:
The graph of this function is shown in the figure below.</span>
</span>
So the problem asks for two conditions:
<em>1. Write the quadratic function in factored form. </em>
<em>2. The vertex has an x-coordinate of 3.</em>
Then the equation (1) must be written as follows:
</span>
To satisfy the two conditions:
So we are free to choose the value of one root, say:
Thus:
Finally, the answer is:
The graph of this function is shown in the figure below.</span>
9514 1404 393
Answer:
138.77
Step-by-step explanation:
Your scientific or graphing calculator will have exponential functions for bases 10 and e. On the calculator shown in the first attachment, they are shifted (2nd) functions on the log and ln keys. Consult your calculator manual for the use of these functions.
The value can be found using Desmos, the Go.ogle calculator, or any spreadsheet by typing 10^2.1423 as input. (In a spreadsheet, that will need to be =10^2.1423.) The result using the Go.ogle calculator is shown in the second attachment.
You can also use the y^x key or the ^ key (shown to the left of the log key in the first attachment). Again, you would calculate 10^2.1423.
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We have assumed your log is to the base 10. If it is base e (a natural logarithm), then you use the e^x key instead. Desmos, and most spreadsheets, will make use of the EXP( ) function for the purpose of computing e^( ). You can type e^2.1423 into the Go.ogle calculator.
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<em>Additional comment</em>
There are also printed logarithm tables available that you can use to look up the number whose log is 0.1423. You may have to do some interpolation of table values. You should get a value of 1.3877 as the antilog. The characteristic of 2 tells you this value is multiplied by 10^2 = 100 to get the final antilog value.
The logarithm 2.1423 has a "characteristic" (integer part) of 2, and a "mantissa" (fractional part) of 0.1423.
