If is a factor of the polynomial, it means that
is a root of the polynomial.
In fact, if a polynomial has a root
(i.e.
), then the polynomial is divisible by
In your case, you know that the polynomial is divisible by , so
is a solution.
Let's evaluate and set it to zero:
We can check the answer: if the polynomial becomes
And we're claiming that is a root of this polynomial:
Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) , (5) 21s and (6) 0, -1, and 5.
Explanation:
Te standard form of the parabola is,
.....(1)
Where, (h,k) is the vertex of the parabola.
(1)
The given equation is,
Comparing this equation with equation (1),we get,
and
Therefore, the vertex of the graph is (5,10) and the fourth option is correct.
(2)
The given equation is,
To make perfect square add , i.e.,
. Since there is factor 3 outside the parentheses, so subtract three times of 9.
Comparing this equation with equation (1),we get,
and
Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.
(3)
The given equation is
To make perfect square add , i.e.,
. Since there is factor 4 outside the parentheses, so subtract three times of 1.
Comparing this equation with equation (1),we get,
and
The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.
(4)
The given equation is,
To make perfect square add , i.e.,
.
Therefore, the correct option is 4.
(5)
The given equation is,
It can be written as,
It is a downward parabola. so the maximum height of the function is on its vertex.
The x coordinate of the vertex is,
Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.
(6)
The given equation is,
Use factoring method to find the factors of the equation.
Equate each factor equal to 0.
Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.
Answer:
(a) The dependant veriable is the $120 per hour and the independant veriable is the $75 consultaion fee.
(b) The table of vaules for this would look like this, , where C = cost and T = time.
(c) The relationship between C and T is linear, beacause with the more hours you take the cost increases.
(d) Yes, it is sensible because the points would be in line due to the steady increase of the hourly rate.
(e) For every hour spent the cost increases 120 dollars.
(f) The fixed cost is 75 dollars for consultation and the veriable cost is 120 per hour.