Question

Graph the inequality

Answer 1

y\[y \le -\frac{ 1 }{ 2 }x ^{2}+x+4\]

Answer 2

Can you show me how you solved it?
I need to also find the
Axis of Symmetry:
Vertex:
y-int:
Is this a graph with a Maximum or Minimum?
Domain:
Range:

Answer 3

I think the y-int is (0,-4) because I got rid of the negative in the the first x term which changed the signs of all the other terms.

Answer 4

Yes, y-intercept is (0,4). To get y-intercept, set x = 0 and compute y.

Answer 5

How is it positive 4?

Answer 6

Would it not be -4 because you get rid of the negative in the first x term?

Answer 7

Since they are asking for vertex, put y = −1/2x^2 + x + 4 in vertex form.
To do that complete the square.

Answer 8

Could you remind me what vertex form is?

Answer 9

y = a(x - h)^2 + k where (h,k) is the vertex.
To put it in vertex form you need to complete the square.

Answer 10

ah ok. Lemme do that real fast for completing the square.

Answer 11

ok so the vertex form I have come up with this now is
y=-2(x-1/2)^2-33/2

Answer 12

Is that correct?

Answer 13

how did the -1/2 coefficient of x^2 become -2?

Answer 14

huh?

Answer 15

U mean the number outside the parenthesis?

Answer 16

yes. original equation has -1/2x^2. If you expand your answer: -2(x-1/2)^2-33/2 you will get -2x^2 ...

Answer 17

I don't ever expand my equation.

Answer 18

Oh wait. I can explain.

Answer 19

My teacher said that if there is a number in front of x^2 in the original equation, to always get rid of it. Thus I divided everything.

Answer 20

What I am telling you is your answer is not correct because -1/2x^2 has now become -2x^2.

Answer 21

yes. This is how I will do it.
Complete the square: −1/2x^2 + x + 4
We want to make the coefficient of x^2 +1. So factor out -1/2. Which means the other terms have to be divided by -1/2 which is same as multiplying by -2:
−1/2x^2 + x + 4 = -1/2(x^2 - 2x - 8)
now complete the square.

Answer 22

Alright so I got a bigger space to work on now,
is this right?
y=-1/2(x-1)^2-9/2

Answer 23

the last term should be +9/2

Answer 24

But I subtracted 9 from both sides..

Answer 25

-1/2(x^2 - 2x - 8)
to complete the square take coefficient of x term and divide by 2: -2/2 = -1.
This -1 will go inside the parenthesis to be squared and you subtract (-1)^2
-1/2(x^2 - 2x - 8) = -1/2{ (x-1)^2 - (-1)^2 - 8 }
= -1/2{ (x-1)^2 - 1 - 8 }
= -1/2{ (x-1)^2 - 9 }
= -1/2(x-1)^2 + 9/2

Answer 26

That is my work..^

Answer 27

The mistake is in the very last line. When you divide -9 by -2, it is +9/2

Answer 28

OHHH!!!!

Answer 29

y = -1/2(x-1)^2 + 9/2
compare this to y = a(x - h)^2 + k which has the vertex at (h,k).
What is the vertex of y = -1/2(x-1)^2 + 9/2

Answer 30

(1,9/2)

Answer 31

I think I have the graph down now. Thank you so much for your help you have no idea how much I needed this :)

Answer 32

you are welcome.