Todd is saving for a vacation. The cost of his vacation is 1,089. Todd has a year to save the money. About how much does he need
2 answers:
Answer:
He needs to save $90.75 each month to reach his goal.
Step-by-step explanation:
We have the cost of his vacation that is $1089.
We know that Todd has a year to save the money.
We know that a year in terms of time is twelve months (12 months).
If we want to calculate how much does he need to save each month we need to divide the total cost of his vacation by the amount of months in a year ⇒
We find that Todd needs to save $90.75 per month to reach his goal.
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Answer:
Step-by-step explanation:
We have the function:
And we want to find x=d for which the minimum/maximum value will occur.
Notice that our function is a quadratic in factored form.
Remember that the minimum/maximum value always occurs at the vertex point.
And remember that the x-coordinate of the vertex is the axis of symmetry.
Since a quadratic is always symmetrical on both sides of its axis of symmetry, a quadratic’s axis of symmetry is the average of the two roots/zeros of the quadratic.
Therefore, the value x=d such that it produces the minimum/maximum value is the average of the two roots.
Our factors are <em>(x-2) </em>and <em>(x-1)</em>.
Therefore, our roots/zeros are <em>x=1, 2</em>.
So, the average of them are:
Therefore, regardless of the value of <em>a</em>, the minimum/maximum value will occur at <em>x=d=1.5</em>.
Alternative Method:
Of course, we can also expand to confirm our answer. So:
The x-coordinate of the vertex is still going to be the place where the minimum/maximum is going to occur.
And the formula for the vertex is:
So, we will substitute <em>-3a</em> for <em>b</em> and <em>a</em> for <em>a</em>. This yields:
Confirming our answer.