Question

Determine the vertex of the given equation.
y = 4x2 + 6x - 1
A.) (-3/4, -5/2)
B.) (5/2, 103/6)
C.) (-3/4, -13/4)
D.) (5/6, 37/18)

Answer 1

There is more than one way you might find the vertex. Is there a particular method you like to use?

Answer 2

You could use x = -b/2a to find the x-coordinate, for example.

Answer 3

If you do that, what is the x-coordinate of your vertex?

Answer 4

Let;s go with x = -b/2a. :)

Answer 5

Ok :)

Answer 6

Or you can put the equation in vertex form if you want to do a few extra steps. ;)

Answer 7

Please let me know what you find for the x-coordinate.

Answer 8

The problem is, I have no idea what to do. My lesson doesn't explain this well. :(

Answer 9

Oh, ok! A quadratic equation is of the form: y = ax^2 + bx + c, where a, b, and c are the "coefficients" or numbers multiplied by your variables.

Answer 10

So, what are a, b, and c for your equation, then?

Answer 11

a = 4, b = ? , c = ?

Answer 12

I'm sorry. :/

Answer 13

Your equation is y = 4x^2 + 6x - 1, so here a= 4, b= 6, and c = -1. Does that make sense so far?

Answer 14

That's ok, if it is new information to you , I don't mind adding extra explanation. :)

Answer 15

Just a moment, though, I have to finish ironing a shirt! BRB

Answer 16

Thanks for waiting!

Answer 17

I don't mind waiting, as long as you help me. :)

Answer 18

So, since a = 4, b = 6, and c = -1 , and since the x-coordinate of the vertex is x = -b/2a, what is -b/2a for your problem?

Answer 19

-6/16?

Answer 20

Close :) -6/8

Answer 21

Which simplifies to what?

Answer 22

-3/4

Answer 23

Yes, so you can eliminate two of your choices, since they don't have an x-coordinate of -3/4

Answer 24

So B and D are tossed out

Answer 25

Okay. :)

Answer 26

You have the x-coordinate of your vertex, x = -3/4 . How would you use that information to find the y-coordinate, do you think?

Answer 27

Plug it into everywhere with an 'x'?

Answer 28

Yes :D

Answer 29

Put it in your equation for x, and then you can find y.

Answer 30

The decimal for this number is -.75, right?

Answer 31

Yes. Please let me know what you get for y.

Answer 32

Okay, thank you for the help. One moment!

Answer 33

Sure!

Answer 34

What do I do with the -1?

Answer 35

Add it at the end. :)

Answer 36

So you have 4(-3/4)^2 + 6(-3/4) - 1 , or 4(-.75)^2 + 6(-.75) - 1

Answer 37

I wouldn't do 4*4? I thought you multiplied the powers?

Answer 38

Yes, for the first term you would square the -3/4 first, and then multiply that result by 4.
So that would give you (-3/4)(-3/4) = 9/16, and then 9/16 X 4/1 = 9/4 or 2.5

Answer 39

This is what I done"
16 (-.75) + 6 (-.75) -1
-12 + 14.5 -1
16.5

Answer 40

You are close to being right. The only thing you did not do was to "square" the -.75 in the first term.

Answer 41

So, it should be 4(-.75)^2 + 6(-.75) - 1
or
4(-.75)(-.75) + 6(-.75) - 1

Answer 42

Since you are not squaring the coefficient (4), but the "x" (-.75)

Answer 43

Okokok. I felt like I was messing up. :p

Answer 44

That's ok :) So if you simplify 4(-.75)(-.75) + 6(-.75) - 1 , that will be our y

Answer 45

And it should match one of the answers. ;D

Answer 46

Please let me know what you get, and I will do the calculation as well.

Answer 47

What is 9/16 in decimal form?

Answer 48

Let's see if you divide 9 by 16, you get 0.5625

Answer 49

That's what I got, I was making sure. :p

Answer 50

Ok, good :D

Answer 51

So then, y = ?

Answer 52

I got -3.25

Answer 53

Good :D

Answer 54

And would -3.25 be -13/4 or -5/2?

Answer 55

-5/2?

Answer 56

Do you have a calculator handy?

Answer 57

I do. :p

Answer 58

You can think of a fraction as being a division (numerator divided by denominator)

Answer 59

So, divide -13 by 4 ; and divide -5 by 2. Which one gives you the answer -3.25?

Answer 60

-13/4 :)

Answer 61

Yes :D

Answer 62

So ... which choice?

Answer 63

C. :)

Answer 64

Yes, C is our perpetrator. ;)

Answer 65

You chose it from the lineup ;)

Answer 66

I hope this was helpful!

Answer 67

That made me laugh! xD

Answer 68

Good! Math should be approached with a sense of humor, I think :D

Answer 69

Keeps you from going nuts while doing it ... I hope!

Answer 70

Have a very good morning, Ms. Alyjoan! I must now hand off the computer. Family computer, so I have to share. :)

Answer 71

Bye! :)

Answer 72

Actually, are you busy, in case I need help again?

Answer 73

I will be available this evening, if that works?

Answer 74

And if you have questions, I will be happy to explain the steps a little better then. :)

Answer 75

Tha'll be fine. :) Thank you!

Answer 76

What time zone, though? I am on the west coast, so Pacific time.

Answer 77

In the evening Pacific time. :)