Question

Complete the first 4 steps for graphing the quadratic function.
y = -x^2 - 4x - 3

Answer 1

Firstly, figure out whether it is maximum or minimum. Is it maximum or minimum?

Answer 2

I don't even know what that means. In my homework, it says nothing about a "maximum" or a "minimum".

Answer 3

this is an algebra question, right? @Biha this is probably different than the Calculus way of graphing. :)

Answer 4

Yes, this is algebra.

Answer 5

y = -x^2 - 4x - 3
y = -(x^2 + 4x + 3)
y = -(x+3)(x+1)

x-intercepts are at x=-3 and x = -1
The vertex is half-way between at x = -2.

Is this correct?

Answer 6

@xo_kansasprincess_xo and @jtvatsim sorry. I was wrong. Actually, I learn the same thing like this in school but with the different concept.

Answer 7

It's okay!:)

Answer 8

that looks correct so far, btw :)

Answer 9

Does the parabola open up or down..?

Answer 10

look at the front of the x^2. If there is a negative sign, then the parabola opens downward. If there is a positive (or nothing), then the parabola opens upward.

You can remember this by thinking -x^2 means the parabola has a "negative" attitude and is sad (opens down). But a positive x^2 means that the parabola has a "positive" attitude and is happy (opens up).

Answer 11

That's a good way to put it

Answer 12

Are those the first four steps? The answer that I posted

Answer 13

4 steps to graph a quadratic equation (not necessarily in order)
1) Find y-intercept. Make x = 0 -> y = ...
2. Find the 2 x-intercepts. Make y = 0. Solve the quadratic equation
-x^2 - 4x - 3 = 0. Since a -b + c = 0, then one real root is (-1) and the other is (-c/a = -3).
3. Find the coordinate of the parabola axis, at x = -b/2a
x = 4/(-2) = -2.
4. Find the min or max. Since a is negative, the parabola is downward, there is a max. Replace x = -2 (coordinate of the parabola axis)
y max = -4 + 8 - 3 = 1

Answer 14

@xo_kansasprincess_xo Also, FYI "min" or "max" is just another way of saying "vertex" -- all of these words are commonly used to describe parabolas, it depends on your textbook. :)

Answer 15

There are also many different "4 steps" to solve parabolas, use whichever method you were taught. :)

Answer 16

1.Determine if the parabola opens up or down.
2.Find the line of symmetry.
3.Find the vertex.
4.Use a table of values to plot a couple of points on each side of the line of symmetry.

^That's what the first four are in my lesson

Answer 17

it kinda similar with what I am going to say . hoho.

Answer 18

OK, you have answer 1 and 2. The line of symmetry is the x = -2 part.

You have almost finished step 3, you just need to find the y value that goes with x = -2.

For step 4, you can pick any x values that you want, plug them in and see what the y values would be. And plot those points.

Answer 19

Lol yeah, but I don't know how to do any of that. That's why I posted the question on here.

Answer 20

OK, the part about finding the y values? Is that the problem? :)

Answer 21

Any of the steps. I didn't actually do the work for those, I found the answers to the first couple steps on the internet because I don't understand how to do this stuff. Plus, I do online school so I don't have any textbooks or anything like that, and it's hard to contact my teacher's.

Answer 22

Oh, OK... that changes things. I thought that the work you posted was yours. :)

Answer 23

hold on just a second, I'm going to find some references. :)

Answer 24

Alright, let's start from the beginning with step 1. Does the parabola open up or down? Do you understand how to determine that based on what we've said so far?

Answer 25

Here's a quick test: Tell us if the parabola opens up or down.

A) x^2 + 3x - 2

B) -3x^2 + 4x + 2

C) -x^2 - 3x - 2

D) 7x^2 -5x + 6

Answer 26

@xo_kansasprincess_xo

Answer 27

In case I have to bail, here is a link to a video explaining how to graph quadratics. They use slightly different methods, but it will get the job done I think: http://www.youtube.com/watch?v=mDwN1SqnMRU