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
Isosceles triangle scalene triangle and equaliteral triangle
Answer: There are 6 pieces of cloth are rectangles and 9 pieces of cloth are triangles.
Explanation:
Since we have given that
For every 5 pieces of cloth, 2 are rectangles
So, remaining piece will be of triangle so,

3 are triangles.
Ratio of rectangles to triangles is 2:3.
Now, she needs 15 pieces of cloth to complete her scarf,
So, Number of rectangles is needed is given by

Number of triangles is needed is given by

Hence, there are 6 pieces of cloth are rectangles and 9 pieces of cloth are triangles.
Answer:
(a) 7 + 3( n - 1 )
(b) 1006
Step-by-step explanation:
ARITHMETIC SEQUENCE.
The number of term of an Arithmetic progression has the formular :
nth term = a + ( n - 1 ) d
a = 7
d = 10 - 7 = 3
nth term = 7 + ( n - 1 ) 3
= 7 + 3n - 3
= 7 + 3( n - 1 )
Therefore,
the nth term of the sequence
= 7 + 3( n - 1 )
(b) For the 1000th term
= 7 + 3 ( 1000-1 )
= 7 + ( 999 )
7 + 999 = 1006
Therefore,
the 1000th term = 1006
1 pizza should cost $5.65
Pizza is $5.65 then bottle of coke is $2.45
3 pizzas and coke: ($5.65*3) + $2.45 = $19.4
I solved this by setting up and solving a system of linear equations:
Variables: p = pizza, c = coke
p = c+3.2
3p+c = 19.4
Solve by substitution
3(c+3.2) + c = 19.4
4c+9.6 = 19.4
c = 2.45
Re-plug in:
p = 2.45+3.2
p = 5.65