Explain two different strategies that you could use to determine the equation of the axis of symmetry defined by y = -2x2 + 16x
- 24. Which strategy do you prefer? Explain why.
1 answer:
<em>Two Strategies</em>
1. Make use of the formula for the axis of symmetry for ax²+bx+c, which tells you that line is ...
... x = -b/(2a)
... x = -16/(2·(-2))
... x = 4
2. Let a graphing calculator show you the vertex, from which the axis of symmetry is easily determined. (See the attachment.) The graph shows the line of symmetry is x = 4.
<em>My Preference</em>
My preference is for the graphing calculator solution (for problems with integer solutions). The one shown is quick and easy and involves no arithmetic. If the coefficients of the equation are not integers, then the formula version is preferred for an exact solution.
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<em>Comment on vertex form</em>
When you put the equation into vertex form, you find a constant for the location of the vertex that is essentially equivalent to -b/(2a). Doing that generally involves three steps: finding b/a, then dividing that in half to get b/(2a), then realizing that the actual vertex location is at the x-value that is the opposite of the one in the vertex-form equation, so is -b/(2a).
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Let h be hamburgers and c be cheeseburgers.
We know that
We also know that
This gives us a system of equations we can solve. My preferred method to solve systems is substitution, where we solve one equation for one of the variables, then substitute that solution in the other equation, reducing it to a single variable equation. One of the equations already equals h, so we can go straight into the sub part.
Finally, we go back to the other equation and solve for h.
So, total there were 253 cheeseburgers sold, and 325 hamburgers sold.
We know that
We also know that
This gives us a system of equations we can solve. My preferred method to solve systems is substitution, where we solve one equation for one of the variables, then substitute that solution in the other equation, reducing it to a single variable equation. One of the equations already equals h, so we can go straight into the sub part.
Finally, we go back to the other equation and solve for h.
So, total there were 253 cheeseburgers sold, and 325 hamburgers sold.
The answer 81pi is if it asked you to keep the answer in terms of pi.
The second answer is if they wanted pi calculated into the answer.
