Question

Determine whether the graph of y = -2x2 - 3x + 10 opens up or down and whether it has a maximum or minimum point.
a.Down and Maximum
b.Down and Minimum
c.Up and Maximum
d.Up and Minimum

Answer 1

First, let us look and see what type of function this is.
\[f(x)=-2x ^{2}-3x+10\]
is a first off a polynomial because it does not have any terms in it that have negative powers. For example, the function \[f(x)=-2x^{-3}+3x\] is not a polynomial, because the variable x has a negative power. Now that we know that the function is a polynomial, we look at the degree. The degree is the highest exponent that the variable has. Because the highest exponent is on the first term, and is \[-2x^{2}\], this is degree of 2 function, also known as a quadratic. Do you know the shape of a quadratic?

Answer 2

I will draw its shape for you.

Answer 3

no i do not):

Answer 4

That is ok, I was trying to draw one on the canvas on here, but it is pretty limited. I will try and post a picture in a minute.

Answer 5

thanks but i still dont knw the awnser ):

Answer 6

This will help you to see why the answer is correct :) I will tell you the answer soon

Answer 7

ooh(:

Answer 8

try to open that

Answer 9

that is a graph of a typical quadratic equation, notice it is a U shaped, and it is opening upward

Answer 10

yes,
i see

Answer 11

That is because, the leading term is positive. If the leading term is negative, it will be a frowny face and will open downward.

Answer 12

ooh,

Answer 13

For example, your graph has a negative leading term

Answer 14

and it is a quadratic, so it should be a frowny face shape (negative is bad, so think negative means frown, means upside down U shape)

Answer 15

Lets graph your function, and see if our prediction is true (it should be opening downward, and have a maximum value)

Answer 16

okay(:

Answer 17

That is a graph of your function, over a random domain (range of x values ) that I chose

Answer 18

As you can see, it is in the shape of a frowny face, so it comes all the way up to a point, and then it starts to decrease again (going from left to right)

Answer 19

So it comes UP to a maximum, and then decreases

Answer 20

So the correct answer, should be a

Answer 21

And the reason is that the term with the highest power of x in it is NEGATIVE

Answer 22

Make sense?

Answer 23

oddly enough yes it does make scene my teacher explains it in the most confusing way possible lol

Answer 24

This is the problem with math teachers haha

Answer 25

Now remember, this shape is only for functions with \[x^{2}\] terms in it

Answer 26

oh okay(: and yes they suck lol

Answer 27

If you have anything higher, for example y =\[x^{3} -2x^{2}\] it will be a different shape, this is because the term with the highest power of x is now 3, not 2

Answer 28

Hope this helped, let me know if you have any other questions.

Answer 29

i just posted one and the guy confused lol

Answer 30

Ahh, I can take a look if you like.

Answer 31

thank you(:

Answer 32

Anytime :)