Question

Help: Quadratic Equations

Attached picture.

Answer 1

Please help

Answer 2

7, 8, and 9 please.

Answer 3

Which questions are you struggling with?

Answer 4

@Compassionate 7, 8, and 9.

Answer 5

Give me a second and I'll take a look

Answer 6

@Compassionate okay thank you. I gave them a try, but I don't think I did them right.

Answer 7

Here is what I could determine from your first problem


3x^2 + 2x - 1 = 0
Roots: -1, 0.33333333333333

Discriminant: 16
Vertex: (-0.33333333333333, -1.3333333333333)
Factored: f(x) = 3(x + 1)(x - 0.33333333333333)
Sum of Roots (-b/a): -0.66666666666667
Product of Roots (c/a): -0.33333333333333

Answer 8

Your actual x solutions are (0, -1)

Answer 9

Your y-intercept would be your vertex. You put your x solutions

Answer 10

3x + 2x - 1
y = -1

Answer 11

So 7 checks out to be good. Now, lets move onto 8. I see you're having trouble finding the vertex

Answer 12

@Compassionate so the y-intercept is -1? would i put (0, -1) ?

Answer 13

So everything i put for #7 is right?
form- standard
y-intercept- (0,-1)
and the axis of symmetry is- -3?

you went so fast that I'm lost lol c:

@Compassionate

Answer 14

Scratch that y-intercept.. if thats my x solutions then what is my y?

Answer 15

Sorry @Compassionate everything is just now loading lol

Answer 16

You got it right. I was picking your brain. Lets go to problem 8. Do you know how to find the vertex?

Answer 17

@Compassionate oh ok :P and no I don't.

Answer 18

You need to get it in standard form first. So, use the FOIL method then multiply by 2

Answer 19

uhh okay.. would I get y=2x^2+2-10 or y=2x^2+2x-10? @Compassionate

Answer 20

\[2x^2 - 8x - 10\]

Answer 21

Now just use the vertex formula

Answer 22

How did you get 8x?

Answer 23

I don't know what the vertex formula is either..

Answer 24

2(x + 1)(x - 5)

2(x^2 - 5x + x - 5)
2(x^2 - 4x - 5)
2x^2 - 8x - 10

Answer 25

ohhhhh! that makes sense.

Answer 26

If I multiply (x + 1)(x - 5) using the FOIL Method (FIRST, OUTER, INNER, LAST)

FIRST: x times x. = x^2
OUTER: x times -5 = -5x
INNER: 1 times x = x
LAST 1 times - 5 = -5

Now I add like terms. -5x + x = -4

So I am left with x^2 -4x - 5

Now I multiply it all by 2 and get 2x^2 - 8x - 10

Answer 27

The formula for the vertex of a quadratic is \[\frac{ -b }{ 2a }\]

Answer 28

okay so -8/2(2)?

Answer 29

which would equal -8?

Answer 30

There are really two formulas you need to remember. The quadratic formula, which will find your roots, and the vertex formula, which finds the lowest or highest point. Think of the vertex as the highest point an object can reach. For example, if I throw a ball at 10 miles an hour, I can find it's max height using the vertex formula. And if I want to know how long it takes the ball to hit the ground, I can use hte quadratic formula and find the roots. Make sense?

Answer 31

\[\frac{ -8 }{ 4 } = 2\] So, so far we have (2, ?). You need to plug 2 into your equation to find y. Then you'll have your vertex

Answer 32

Oh, and I think I made a mistake. It's -(-8)/2(2) that's how I got 2. Because the formula is

-b/2a, so if I have -(-8)/2(2) the -8 becomes positive 8 over 4. Which is 2

Answer 33

i thought -b/2a was the axis of symmetry for some reason. but yes i get it.

and okay so 2(2)^2-8(2)-10=-18?

I feel like I'm doing this all wrong..

Answer 34

Nope! You got it right. You've been right so far.

So yup, your vertex is (2, -18)

Answer 35

Okay so the form is intercept form, the x-intercept is (-1,5) and the vertex is (2,-18)? @Compassionate

Answer 36

Precisely.

Answer 37

Ready to do your last one?

Answer 38

yes :)