First of all to transfer <span>(2x - 1)(x + 6) = 0 into a form where we can plug it into the quadratic formula we need to use the FOIL method.
</span><span>(2x - 1)(x + 6) = 0
</span> becomes
2x*x+2x*6+-1*x+-1*6
which simplifies to
2x^2 + 12x - x - 6
and then we add like terms to get
2x^2 + 11x - <span>6
</span>
now that it is in the correct form we can identify "a" "b" and "c" by following this form
ax^2 + bx + c
looking back at the equation we got earlier
2x^2 + 11x - <span>6</span>
a=2,b=11,and c=-6
Part A:
Given the function

, the absolute maximum or minimum occurs when

.

Using the second derivative test,

Since the second derivative gives a negative number, the given function has a maximum point at

.
And the maximum point is given by:

i.e.

Part B:
Given the function

, the absolute maximum or minimum occurs when

.

Using the second derivative test,

Since the second derivative gives a negative number, the given function has a maximum point at

.
And the maximum point is given by:

i.e. (0.693, 0.25)
<span>the coordinates of the vertex of the f(x) is (2 , -3)
and when f(x) is converted to g(x) the coordinates of the vertex [ vertex of g(x) ] has become ( 7 , -7)
when f(x) transformed to g(x)
the x coordinates has increased by +5 any y coordinates has change by -4
i mean when
( 2 , -3) ----> ( 7 , -7)
so the answer is
(x, y) → (x + 5, y – 4)
hope this will help ya !!</span>
Answer:

Step-by-step explanation:
Number of students in senior class is 130
<em><u>Solution:</u></em>
Given that Every student in the senior class is taking history or science
85 of them taking both history and science
106 seniors takes history
109 seniors takes science
To find: number of students in senior class
Let A be the set of the students of the senior class that take history
Let B be the set of students of senior class that they science
The number of students in senior class is given by:

Where,
A = 106 and B = 109 and |A n B| = 85

Thus number of students in senior class is 130