Question

Part 1:
Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. Show your work to receive full credit.

y = x2 + 3x + 2
y = x2 + 2x + 1
Part 2:
Using complete sentences, answer the following questions about the two quadratic equations above.
Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 3x + 2 different from y = x2 + 2x + 1?

Answer 1

y = x^2 +3x + 2
y = x^2 +2x +x +2
y = (x+2)(x+1)
0 = x+2, x= -2
0 = x+1, x= -1
X intercepts are at (-2, 0) and (-1, 0)

y = x^2 + 2x + 1
y = x^2 +x +x +1
y = (x+1)(x+1) or y = (x+1)^2
0 = x+1, x= -1
X intercept is at (-1,0)

Both equations represent parabolas, and both cross the X axis at (-1,0).
The first equation has possible negative x values whereas the second does not.

Answer 2

thts 1st part

Answer 3

oh hahaha thankya

Answer 4

In addition to that, they have different factors.

Similarities
1. Both quadratics
2. Both intersect at same point (-1,0)

Differences:
1. Different axes of symmetry
2. Different x and y intercept
3. Different factors

Answer 5

thts it

Answer 6

the writing from the 1st part i gave u and this also is part 2

Answer 7

and part 1

Answer 8

May I help ?:)

Answer 9

Solve 3x2 = 12x.

x = 0, x = 4

x = 0, x = −4

x = 3, x = 4

x = 3, x = −4

Answer 10

wait... let me check part 2 fully

Answer 11

ok and this is aprt 2: The two equations share the following common properties: They both have a root at x = -1. They also both open upwards. The difference between the two equations is that the second equation is a perfect square which is tangent to the x-axis at (-1,0) and does not take on any negative values. The equations both have distinct turning points and axis of symmetry.

Answer 12

x = 2, x= -2

Answer 13

o 12xz

Answer 14

x = 0, x=4

Answer 15

there u go

Answer 16

3x^2-12x+0=0
So we have Quadratic equation .
So use from Delta and find x1 and x2 .

Answer 17

What are the solutions of 6x2 + 7x – 5 = 0? solve for the x's

Answer 18

x = negative 5/3, x = 1/2

Answer 19

Identify which equation is a quadratic equation.

y = −5x − 3

y = −4x(x + 10) + 34

y + x2 = (x − 4)(x + 3)

y − 2 = (x − 2)(x2 + 1)

Answer 20

y = −4x(x + 10) + 34

Answer 21

wait let me double check

Answer 22

@samsterz : i think say the formula is better .

Answer 23

yes its y = −4x(x − 4) + 2x

Answer 24

Determine whether the graph of y = 3x2 − 7x + 2 opens up or down and whether it has a maximum or minimum point.

Down and Maximum

Down and Minimum

Up and Maximum

Up and Minimum

Answer 25

wait lolol wrong math

Answer 26

@jordynnn : Do u know that formula ???

Answer 27

no, i suck at math :(

Answer 28

jordynn did u submit a quiz or something, if so what did u get prior?>

Answer 29

answer is : Up; Minimum

Answer 30

i havent submitted anything yet

Answer 31

lol it must be long

Answer 32

When the quadratic equation y = (x − 2)(3x + 1) is written in standard form, what is the value of the coefficient "b"?

−5

3

−2

5

Answer 33

omg it is

Answer 34

answer is A: -5

Answer 35

What is the vertex for the graph of y = −2x2 + 8x − 13?

(2, 11)

(2, −5)

(−2, −37)

(−2, −21)

Answer 36

(2, −5)

Answer 37

What are the solutions of x2 − 3x − 18 = 0?

x = 3, x = −6

x = −3, x = 6

x = 3, x = 6

x = −3, x = −6

Answer 38

@samsterz : What are you doing ??????

Answer 39

?? what do u mean

Answer 40

is it C?

Answer 41

You just answer to her .
She can learn them ...

Answer 42

x= -3, x=6

Answer 43

lololol

Answer 44

What are the x-intercept(s) of the graph of y − x2 = 11x + 30?

(−5, 0) and (6, 0)

(5, 0) and (−6, 0)

(−5, 0) and (−6, 0)

(5, 0) and (6, 0)

Answer 45

its greatly appreciated that @samsterz is helping me

Answer 46

x intercepts (-6,0),(-5,0)

Answer 47

im on the last one now!!

but its long again .. ;/

Answer 48

lol show it

Answer 49

Part 1: Solve each of the quadratic equations below. Show your work. (3 points)

x2 − 25 = 0 and x2 = 2x + 15

Part 2: Describe what the solution(s) represent to the graph of each. (2 points)

Part 3: How are the graphs alike? How are they different? (2 points)

Answer 50

1st part : x2-25=0
(x+5)(x-5)=0
x=-5 or x=5

x2=2x+15
x2-2x-15=0
(x-5)(x+3)=0
x=5 or x=-3

part 2 and 3:
2. The values of 'x' are the points on the x-axis where the curve intercepts(crosses) .

3. They are both 'bowl' shaped.
They both have the same coefficient of 'x^2' so they both have the same degree of 'closure'.
The first has a minimum at x = 0 and y = -5
The second has a minimum at x = 1 and y = -16 . It also intercepts the y-axis at y = -15.

This graph opens down. I know because it has a negative number with the x^2 term.
The graph has a maximum, as do all graphs that open down.
The vertex is at (0.7, 0.45)
The x-intercepts are at (0.4, 0) and (1, 0)

Answer 51

there was a second one to it that i forgot

Answer 52

Create your own unique quadratic equation in the form y = ax2 + bx + c. Use complete sentences and show all work to determine the following:

Does the graph open up or down? How do you know? (2 points)
Explain whether the graph has a maximum or minimum point. (2 points)
Find the vertex and x-intercepts of the graph. (3 points)

Answer 53

Here's one for you:
y = x^2 - 8x + 12 This factors as y = (x - 6)(x - 2)
So, x-intercepts are at (6, 0), and (2, 0)
This opens up because the implied "a" value is 1.
It also has the vertex form of y = (x - 4)^2 - 4 so it has a vertex at (4, -4) and it is at this point where the graph and equation has its low-point.

done.

Answer 54

lol :P

Answer 55

i got a 92% :D

Answer 56

;(

Answer 57

i missed like 2?

Answer 58

no, i did some before asking you, you got them ALL

Answer 59

hopefully ur score will go up when u the teacher grades written

Answer 60

good luck

Answer 61

you're amazing thankyou so much! :)

Answer 62

yup, trying to do some good deeds