Is this correct? (Geometry hw)
2 answers:
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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.
Answer:
Rational, Rational, Rational, Irrational, Irrational
Step-by-step explanation:
The first question:
- -√49
- -7
This number is rational
Second:
- -70.8888....
This number is rational. It wouldn't be rational if the digits won't repeat.
Third:
- 15.91
This number is rational
Fourth:
- 17π
This is irrational. The digits of pi do not repeat, making it irrational.
Fifth:
- -√14
Irrational. The square root of a non-perfect square is irrational.
<h3 />-Chetan K
