Question

Choose all of the following equations that have a graph in which the parabola opens downward. More than one answer may be chosen.

y = 2x^2 + 2x + 8

y = −4x^2 + 8x − 19

y = 16x^2 + 2x − 4

y = −x^2 − 6x + 10

Answer 1

parabola is a quadratic function...that means the equations with square

downward means negative coefficient of x^2

Answer 2

Oh man.. that word.

Answer 3

Coefficients.

Answer 4

throws me off everytime.

Answer 5

Coefficient of any variable in a term is the number you are multiplying the variable with :)

Answer 6

coefficient is the number beside x lol

Answer 7

For example, the coefficient of x in 4x is 4, and the coefficient of 4 in 4x is x.

Answer 8

left side or right side?

Answer 9

gtg late for class...you get it though..right @careless850 ??

Answer 10

I'll never get it. :/

Answer 11

Thanks though.

Answer 12

the number on the right is the exponent..the left is the coefficient

Answer 13

Okay so what does coefficients have to do with this again?

Answer 14

So the answers are B and D?

Answer 15

Yes.

Answer 16

Ahh...

Answer 17

So if these are - squared then it opens downward. If they are + it's a U.

Answer 18

Yes. Do you know about maxima and minima?

Answer 19

Choose all of the following equations that have a vertex that is the minimum point of the parabola. More than one answer may be chosen.

y = 2x2 + 2x + 8

y = −16x2 + 2x − 4

y = −x2 − 4x − 3

y = x2 + 2x + 4

Answer 20

Just got to those. Lol.

Answer 21

It is directly related.
If a quadratic, N, opens down, it has a maxima.
If a quadratic, P, opens up, it has a minima.

http://www3.wolframalpha.com/Calculate/MSP/MSP30601a1hbiag5d670d4100001hhh30h2fgf00h41?MSPStoreType=image/gif&s=47&w=299&h=130&cdf=RangeControl

This is a quadratic that opens downward. Do you see how it has a maxima? In other words, how it has a maximum value?

http://www3.wolframalpha.com/Calculate/MSP/MSP22531a1hc11hcci924d300000g2h9ag0b56c518b?MSPStoreType=image/gif&s=45&w=299&h=139&cdf=RangeControl

This is a quadratic that opens upward. Do you see how it has a minima? In other words, how it has a minimum value?

Answer 22

Minimas are wider U ... and maxima are wider upside down u.

Answer 23

or no

Answer 24

wait

Answer 25

they go x from -1 to 1.

Answer 26

Not quite.
A quadratic *has* a minima. But it only has a minima if it opens upward.

Likewise, a quadratic *has* a maxima. But it only has a maxima if it opens downward.

(The pictures are just the typical example.)

Can you answer your question now? :)

Answer 27

A & D.

Answer 28

Good job! :D