4. 1 less than twice the square of a number
1 answer:
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Answer:
The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is .
Step-by-step explanation:
From Fundamental Theorem of Algebra, we remember that the degree of the polynomials determine the number of roots within. Since we know three roots, then the factorized form of the polynomial function with the lowest degree is:
(1)
Where ,
and
are the roots of the polynomial.
If we know that ,
and
, then the polynomial function in factorized form is:
(2)
And by Algebra we get the standard form of the function:
(3)
The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is .
In the given question, is shifted one unit to the right of
So, Option C is correct.
Step-by-step explanation:
The parent function is and transformed function is
So, Parent Function:
Transformed Function:
- If transformed function is of type: g(x) = f(x-h), then the graph is shifted to right h units.
So, In the given question, is shifted one unit to the right of
So, Option C is correct.
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Answer:
C. is your answer
Step-by-step explanation:
In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is
,
where x = h is the equation of the line of symmetry.
To get this into vertex form we will complete the square. The first couple of steps I will combine into 1. We will set the quadratic equal to zero, then move the constant over to the other side:
The next rule is that the leading coefficient HAS to be a positive 1. Ours is a positive 88, so we have to factor it out:
Now we can perform the process of completing the square. The rule is to take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2, and 3/2 squared is 9/2. We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored. It serves as a multiplier into the parenthesis. What we actually added in, then, was 88(9/2) which is 198:
The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex. We will state that binomial and at the same time do the addition on the right:
Now we can move the constant back over and set it back equal to y:
From that form you can see that the equation of the line of symmetry is x = 1.5. The coordinates of the vertex are (1.5, 102). If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.
C then is your answer.