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viva [34]
3 years ago
5

The table shows values of a function f (x) . HELP

Mathematics
1 answer:
maw [93]3 years ago
4 0

Answer:

The average rate of change is 4

Step-by-step explanation:

The average rate of change of the function over the interval is given by the slope of the line that connects the points;

(5,-2) and (9,14)

The slope of a line given 2 points is calculated as;

change in y/change in x = (14- -2)/(9-5)

                                        = 16/4

                                        = 4

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What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negati
Anestetic [448]
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

6 0
3 years ago
Help and i will make brainliest and will than and rate and give points if someone helps me
Marysya12 [62]
1.
8{c}^{2} - 1.5d \\
2.
6 - 4x
3. -7/30
4. i believe it is the communitive of multiplication , but not 100% sure
6 0
2 years ago
Solve the equation.
aksik [14]

Answer:

x = -1

Step-by-step explanation:

\frac{2}{3} - 4x + \frac{7}{2} = -9x + \frac{5}{6}

Add 4x to each side of the equation

\frac{2}{3} - 4x + \frac{7}{2} + 4x = -9x + \frac{5}{6} + 4x

\frac{2}{3} + \frac{7}{2} = -9x + \frac{5}{6} + 4x

Subtract ⅚ from each side

\frac{2}{3} + \frac{7}{2} - \frac{5}{6} = -9x + \frac{5}{6} + 4x - \frac{5}{6}

\frac{2}{3} + \frac{7}{2} - \frac{5}{6} = -9x + 4x

\frac{4 + 21 + 5}{6} = -5x

\frac{30}{6} = -5x

5 = -5x

Divide both sides by -5

\frac{5}{-5} = \frac{-5x}{-5}

-1 = x

x = -1

8 0
2 years ago
9x² - 12x + 4 <br><br>pls need ans.​
kolezko [41]

Step-by-step explanation:

\tt{9 {x}^{2}  - 12x + 4}

Here, the second order of polynomial ax² + bx + c is factorized and expressed as the product of two linear factors. First, we have to find the two numbers that adds to 12 and if we multiply those numbers , we get 36 ( The two numbers should be 6 and 6 ).

⟶ \tt{9 {x}^{2}  - (6 + 6)x + 4}

⟶ \tt{9 {x}^{2}  - 6x - 6x + 4} { Distribute x through the parentheses )

⟶ \tt{ \underbrace{9 {x}^{2}  - 6x}} \:  -  \underbrace{6x + 4}

⟶ \tt{3x(3x - 2) - 2(3x - 2)}

⟶ \tt{(3x - 2)(3x - 2)}

⟶ \tt{ {(3x - 2)}^{2} }

\pink{ \boxed{ \boxed{ \tt{ Our \: final \: answer :  \boxed{ \underline{ \tt{{(3x - 2)}^{2} }}}}}}}

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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4 0
3 years ago
42 liters of juice were evenly
I am Lyosha [343]

Answer: 42/6=7

Step-by-step explanation:

there's 42 liters of juice right? so to <u>divide</u> it into six batches all you got to do is divide all the liters of juice into how many batches you need. So as it says in the question, just divide 42 by 6 and you'll get your answer which is 7.

5 0
2 years ago
Read 2 more answers
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