Question

The graph of y = 3x2 + 4x − 7 is shown below. What are the zeros of the function (as exact values), the y-intercept, and the maximum or minimum value of the function (rounded to the nearest tenth)?

Hint: Use a graphing utility or rewrite the function in different forms to help you answer these questions.

The graph of the parabolic function y equals three times x squared plus four times x minus seven

Answer 1

Zeros: x equals negative start fraction seven over three end fraction comma 1; y-intercept: (0, −7); minimum: −8.3
Zeros: x equals start fraction three over seven end fraction comma −1; y-intercept: (0, −7); maximum: −8.3
Zeros: x equals start fraction seven over three end fraction comma −1; y-intercept: (0, 7); maximum: −0.7
Zeros: x equals negative start fraction three over seven end fraction comma 1; y-intercept: (0, 7); minimum: −0.7

Answer 2

@Nnesha

Answer 3

@ParthKohli @sammixboo @sleepyhead314

Answer 4

@Data_LG2 @freckles @timo86m

Answer 5

I can help.

Answer 6

@Maddy1251 think you can help some more I was able to take a break after finishing two assignments so now I'm back with a different one.

Answer 7

oh your backlol

Answer 8

welcome to 60 ss btw

Answer 9

Thank ya :-)

Answer 10

I pointed out your zeros.

Answer 11

x=-2.333 and x=1

Answer 12

ok

Answer 13

x=-7/3 instead of -2.333

Answer 14

A is your answer.

Answer 15

y=3x^2+4x-7
That -7 at the end tells us what our y-intercept is,
y=(0,-7)

Answer 16

:o that was fast and ok yeah I was just reading what you wrote.

Answer 17

It has a minumum point of x=-0.667 y=-8.333

Answer 18

Zeros: x equals negative start fraction seven over three end fraction comma 1; y-intercept: (0, −7); minimum: −8.3
Looks like this matches pretty good.

Answer 19

ahhh thanks I was about to ask how to get 8.3 but you just explained it so... !D

Answer 20

Yes, its a parabola, so the bottom of the parabola is our minimums. You'll learn more of that in calc.

Answer 21

It would have maximums if the parabola was flipped, I believe, such as opening downwards.

Answer 22

Where the U of the parabola would be in the positive quadrants. I could be wrong, I'm dusting the cobwebs off my algebra skills folder today, haha.

Answer 23

haha ok ...

Answer 24

Hope that all makes sense.

Answer 25

Ill be back on later I dont want to hold you up ... i have to do the dishes real quick. But i read your stuff and i think i get it.

Answer 26

Great, you're not holding me up :-) Just want to make sure you get it. If not let me know

Answer 27

@Maddy1251 yeah thats right im back! the kid returns lol... to much... yeah to much i need a better take away on my intro xD. anyways ready to help me do a few more. After these next three your free and can have a happy day. :`>

Answer 28

No your intro is better than anything I could make up xD Yes of course I will help, I love to help you!! Please, as many questions as you need hep with I am here to help. :-)

Answer 29

well that sounds fantastic because I actually had four more but i was going to be nice and do the last one myself.

Answer 30

What is the equation of the quadratic function graphed below?

Graph of a parabolic function coming up from the left through the point approximately at negative two and three fourths comma zero and turning at the point negative one comma nine and going down through the point zero comma six and through the point at approximately three fourths comma zero and continuing towards negative infinity.

y = 3(x − 1)2 − 9
y = −3(x + 1)2 + 9
y = −3(x − 1)2 − 9
y = 3(x − 9)2 − 1

Answer 31

so this one is pretty similar too just different solutions.

Answer 32

theres my graph.

Answer 33

Thank you for the picture :D

Answer 34

Its opening downward, so our slope will be Negative. So that takes out A and D

Answer 35

Our y-intercept looks to be 6 on the positive side of the y-axis.

Answer 36

yes just about to say that.

Answer 37

Soo I am going to simplify out B and C to see if any of these two equations will give me my desired answer.

Answer 38

Excellent!

Answer 39

I shall start with this one ; y = −3(x + 1)2 + 9

Answer 40

hmm so can I just plug in each equation? or something else?

Answer 41

oh ok

Answer 42

I want it to look like ;
y=mx+b

Answer 43

3x + 1^2 + 9??

Answer 44

well actually 3x + 3^2 +9* not 1 because I think I distribute both.

Answer 45

I have one question

Answer 46

y = −3(x − 1)2 − 9
Does it actually look like this?
\[y=-3(x-1)^{2} -9\]

Answer 47

yes

Answer 48

Ah okay, no wonder why I wasn't getting any right answers!

Answer 49

:O

Answer 50

y = −3(x − 1)2 − 9
-3(x-1)(x-1)-9

Answer 51

yep yep

Answer 52

(x-1)(x-1)=\[x^{2}-1x-1x+1\]

Answer 53

like terms? do anything with them?

Answer 54

\[x^{2}-2x+1\]

Answer 55

Look right?

Answer 56

ah you did do something with the like terms. ok proceed, and yeah so far.

Answer 57

:-)\[y=-3(x^{2}-2x+1)-9\]

Answer 58

Look okay?

Answer 59

yep, yep.

Answer 60

\[y=-3x^{2}-6x-3-9\]

Answer 61

oh alright.

Answer 62

One minute.. As of right now its in perfect parabola form.Combine like terms for me please.

Answer 63

since there all negatives this will mostly be positives i guess.

Answer 64

I think I figured it out but please continue.

Answer 65

oh okay didnt see that part well just give me a minute.

Answer 66

ok so the 3 and 9 are like terms so -3 -9 = -12?

Answer 67

so it would like this now? 3x^2 - 6x - 12? yes or did I mess up.

Answer 68

I assume i messed up because its suppose to end with a 9. negative or positive but still a 9 and I got a 12.

Answer 69

you still there @Maddy1251

Answer 70

Just got back

Answer 71

Yes it will be -12

Answer 72

oh ok

Answer 73

\[-3x^{2}-6x-12\]

Answer 74

When I graphed this, my line was all the way down by (0,-12)

Answer 75

So, we will proceed with the next equation

Answer 76

\[ y = −3(x + 1)^{2} + 9\]

Answer 77

\[(x+1)^{2}=(x+1)(x+1)=x^{2}+1x+1x+1\]

Answer 78

\[x^{2}+2x+1\]

Answer 79

So now\[y=-3(x^{2}+2x+1)+9\]

Answer 80

Pretty sure that's it. Anyways, distribute -3

Answer 81

\[-3x^{2}-6x-3+9\]

Answer 82

yes thats it your clarified my answer so it was that :D. thanks.

Answer 83

\[y=-3x^{2}-6x+6\]

Answer 84

Would you look at that. A negative slope, the x is squared to give us the parabola, and we have the '+6' to verify our y-intercept

Answer 85

We can graph this now.

Answer 86

cool ok

Answer 87

Boom, there is our answer!

Answer 88

B is your answer.

Answer 89

yes it was right :~> :`>


Ok next one way less tough and I believe that this is B also if were talking simpliest form. ofcourse I could be wrong.



What is the equation, in vertex form, of the quadratic function that has a vertex at V(6, −7) and passes through point P(4, −9)?

y equals start fraction one over two end fraction left parenthesis x plus six right parenthesis squared minus seven
y = −2(x − 6)2 − 7
y equals negative start fraction one over two end fraction left parenthesis x minus six right parenthesis squared minus seven
y equals start fraction one over two end fraction left parenthesis x plus six right parenthesis squared minus seven

Answer 90

Do you know what vertex form is?

Answer 91

wait dint read that yet.. its to messy i can separate this real quick.

Answer 92

y equals start fraction one over two end fraction left parenthesis x plus six right parenthesis squared minus seven

y = −2(x − 6)2 − 7

y equals negative start fraction one over two end fraction left parenthesis x minus six right parenthesis squared minus seven

y equals start fraction one over two end fraction left parenthesis x plus six right parenthesis squared minus seven
there much better.

Answer 93

and no I am not sure im familiar with vertex yet. Well in math terms no the regular meaning yes.