FIND THE QUADRATIC FUNCTION DETERMINED BY EACH TABLE
X -2 -1 0 1 2 3
Y 4 0 -2 -2 0 4

Answer:

x² - x - 2 = 0

Step-by-step explanation:

plotting the graph of x and y,we have that the root of the equation is -1 or 2

x = -1 or 2

the eqn therefore is;

x² - (sum of the root)x + (product of the root) =. 0

x² - (-1+2)x + (-1*2) = 0

x² - x - 2 = 0

Applying the Factor Theorem, it is found that the quadratic function is:

[tex]p(x) = x^2 - x - 2[/tex]

------------------------

The Factor Theorem states that if a polynomial [tex]p(x)[/tex] has roots [tex]x_1, x_2, ..., x_n[/tex], it is described by the following equation:

[tex]p(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]

In which a is the leading coefficient.

[tex]p(x) = a(x - (-1))(x - 2)[/tex]

[tex]p(x) = a(x + 1)(x - 2)[/tex]

[tex]p(x) = a(x^2 - x - 2)[/tex]

When x = 0, p(x) = -2, and we use this to find a.

[tex]p(x) = a(x^2 - x - 2)[/tex]

[tex]-2 = a(0^2 - 0 - 2)[/tex]

[tex]2a = 2[/tex]

[tex]a = \frac{2}{2}[/tex]

[tex]a = 1[/tex]

Thus, the quadratic function is:

[tex]p(x) = x^2 - x - 2[/tex]

A similar problem is given at https://brainly.com/question/24380382

3g-2+7g+8=
What is this

Please help me! Im not good at this topic.

please help me out with this question.
much appreciation. Thanks.​

Jack has 27 pencils. Shane has 3 more than twice the amount that Jack has. Which equation shows the relationship between the number of pencils Jack (j) has and the number of pencils Shane (s) has?

Sam has a total of 43 quarters and nickels in her purse. If her change is worth $7.75, how many nickels and how many quarters does Sam have?
Warning: This is Algebra 1

ILL GIVE BRAINLIST IF YOU ARE RIGHT 1. (05.01 LC)
The graph shows the distance, y, that a car traveled in x hours:

What is the rate of change for the relationship represented in the graph? (1 point
55
54
1/54
1/55

a necklace contains 36 gram of gold 72% of the mass of necklace is gold what is the mass of the necklace

Evaluate the expression | 9 | + | - 2|

Rosa picked some peaches from one tree,
and then she picked 8 peaches from a
different tree.
She gave 10 peaches to Sten.
She has 12 peaches left.
How many peaches did Rosa pick from the
first tree?

Rewrite the expression by collecting like terms.
1/2k - 3/8k

Helppp ASAP plzz!!! Hurry

If Gabe's Soccer Ball Company is able, due to competitive pressure, to charge $60 for a new soccer ball, while one soccer ball costs $28 to make, plus $15,000 per month in overhead costs (mostly Gabe's extravagant salary) find: a. The average cost c(x) of producing each soccer ball b. Algebraically find the number of soccer balls Gabe's company must produce per month in order to break even (Profit = 0). Profit = Total Revenue – Total Cost c. Algebraically find the number of soccer balls Gabe's company must make to earn a profit of $10,000 per month. d. If Gabe took a pay cut to reduce the overhead costs to $8,000 per month, how many fewer balls would the company have to sell to break even. (There are multiple ways to get this result).

Arrange the decimals from least to greatest. Choose the letter below that shows the order least to greatest.

-4.3 -0.43 -0.043 -0.34 -3.4

-4.3, -3.4, -0.43, -0.34, -0.043

-4.3, -0.43, -0.043, -3.4, -0.34

-0.043, -0.43, -0.34, -3.4, -4.3

Solve the simultaneous equations:

3a-2b=14
12a+9b=39

In 1992, Disney created a one-of-a-kind special pin. Each year, the pin’s value appreciates by a constant amount. In 1997, the pin was valued at $350. In 2002, it was valued at $600. Let x be the number of years since 1992 and y be the value of the pin in dollars. Write a linear equation in slope-intercept form that models this situation.

In order for two figures to be considered similar, which of the following MUST be true? (Check all that apply) There is more than one answer.


Corresponding sides are proportional


Corresponding sides are congruent


The shapes are exactly the same in side length and angle measure


Corresponding angles are congruent

Please answer this giving brainliest and 20 points. If you say something weird i will make sure you get banned.

I need help with this question ASAP

Sara borrows $56 from her mother to buy a new pair of jeans. If
Sara decreases her debt by $4 each week, how many weeks will
it take her to pay off the whole amount she owes her mother?

The cost y (in dollars) to spend an evening bowling is proportional to the
number of games x that are bowled.
It costs $16 to bowl 4 games.
5. Write an equation that represents the situation.
6. How much does it cost in dollars) to bowl 6 games?

Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?

Can I please get some help with this :D

What is 1232456 * 789456? I will mark brainliest!!

which is closer to 0 3/8 or -1/3

Xochitl has saved $201.60. Yamka has saved LaTeX: \frac{2}{3}2 3 the amount Xochitl saved. Zack has saved 1.5 times the amount Yamka saved. How much have they saved all together?

Find the slope of the line passing through the points (9,3) and (9,-5).

Math Trick
43 x 67 = ?

Which graph represents the equation 6x−5y=10 ? A image 1ab24067a1a445c6b2cc4633bfedfbb0 B image 28e91cd406af4c89bbd5cef1ec880a48 C image cfe6c7f17af74557ac6084f98e5bf5e0 D image 6fe8450f191547f885106542b28826f1

Which values from the given replacement set make up the solution set of the inequality?

m+7<18 ; {8, 9, 10, 11}

{9, 10, 11}

{8, 9, 10}

{8, 9}

{10, 11}

Can anyone help me on these 2 questions