A parabolic function's key characteristic is either having 2 x-intercepts or 2 y-intercepts. That is the reason why the standard form of parabolic functions are:
(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where
(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex
This is also called vertex form because the vertex (h,k) is grouped according to their variable.
Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be
y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.
The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1
To find the zeros of this function, we must first set the entire function equal to 0
f(x) = x² - 2x - 15 = 0
Since this is a quadratic function, we must use the quadratic formula, which is:

Let's assign a, b, and c using our first function
x² means a = 1 (because it could be written as 1x²)
-2x means b = -2
-15 means c = -15
Now let's plug those in:

which simplifies to:

Simplified further:


And divide it by the 2 on the bottom gives us:

2+4 = 6
2-4 = -2
So the zeros of this function are
-2 and
6
Step-by-step explanation:
There are 2 questions in one.
1)
<u>Roberta is 20 years older than Julian. In 4 years, Roberta's age will be twice Julian's age:</u>
---------------------------
2)
<u>Roberta is twice as old as David. In 10 years, Roberta will be 8 less than three times David's present age:</u>
Correct choice is A
I think it should be 6.5 inch but I'm not positive.
I hope this helps! :))
Answer:
8 Gallons Per Minute
Step-by-step explanation: