The GCF of seven and 21 is

The graph of a quadratic function passes through the points (-1,0), (-2,0), and (0,2). Write the quadratic function in general f

ddd [48]

Answer:

$f(x)=x^2+3x+2$

Step-by-step explanation:

step 1

we have the points

(-1,0), (-2,0), and (0,2)

Plot the points

using a graphing tool

see the attached figure

The graph of a quadratic function must be a vertical parabola open upward

The vertex is a minimum

The quadratic function in general form is equal to

$f(x)=ax^2+bx+c$

Substitute the value of x and the value of y of each given ordered pair in the general equation and solve for a,b and c

(0,2)

For x=0, y=2

substitute

$2=a(0)^2+b(0)+c$

$c=2$

(-1,0)

For x=-1, y=0

substitute

$0=a(-1)^2+b(-1)+2$

$0=a-b+2$ ----> $a=b-2$ ----> equation A

(-2,0)

For x=-2, y=0

substitute

$0=a(-2)^2+b(-2)+2$

$0=4a-2b+2$ ----> equation B

we have the system

$a=b-2$ ----> equation A

$0=4a-2b+2$ ----> equation B

substitute equation A in equation B

$0=4(b-2)-2b+2$

solve for b

$0=4b-8-2b+2$

$2b=6$

$b=3$

Find the value of a

$a=3-2=1$

therefore

The quadratic function in general form is equal to

$f(x)=x^2+3x+2$

see the attached figure N 2 to better understand the problem

7 0

3 years ago

Answer this equation -3(5g+1)+8g=

maksim [4K]

Answer:

-7g - 3

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Combining like terms

Step-by-step explanation:

Step 1: Define expression

-3(5g + 1) + 8g

Step 2: Simplify

Distribute -3: -15g - 3 + 8g
Combine like terms: -7g - 3

6 0

3 years ago

Read 2 more answers

Find the exact value of sin(20) using the double-angle formula given: sin(0) = -4/5 , π<0<3π/2

viktelen [127]

Answer:

I think its A

Step-by-step explanation:

Sin(20) = 0.91294525072 which in a fraction it would be 24/25

5 0

3 years ago

Advertising A bank manager wants to encourage new customers to open accounts with principals of

schepotkina [342]

Answer:

The poster say, "Open an account of $3,500 and earn at least $10 interest in 1 month!" is correct

Step-by-step explanation:

Given, A bank manager wants to encourage new customers to open accounts with principals of at least $3,500.

He decides to make a poster advertising a simple interest rate of 4.8%.

We have to find what must the principal be if the bank manager also wants to advertise that one can earn $10 the first month

We know that, banks offer simple interest

In our problem, simple interest = $10, rate = 4.8%, time = 1 month

Let us see Can the poster correctly say, "Open an account of $3,500 and earn at least $10 interest in 1 month!"?

So now, in our problem, amount = $3500, rate = 4.8% and time = 1 month =

So, the statement is correct.

Hence, amount to be invested is $2500 and poster says correctly.

5 0

3 years ago

Here is a table of values y = f(x)

Rama09 [41]

A. Yes, the value of this function is 8 when x is 15.

B. False. I noted right away that the ordered pair (0,5) is not included, and some of the ordered pairs included do not represent the given function.

C. Yes, f(5) = 6. See (A) above.

D. False. The range of this function is the set of integers between 5 and 13 inclusive.

4 0

4 years ago