Which of the following quadratic functions has a graph that opens downward? Check all that apply.

A. y=2x-x^2
B. y=1/3x^2-8x-13
C. y=2/3x^2-13x+5
D. y=-(3+x^2)

Question

Which of the following quadratic functions has a graph that opens downward? Check all that apply.

A. y=2x-x^2
B. y=1/3x^2-8x-13
C. y=2/3x^2-13x+5
D. y=-(3+x^2)

anonymous · Answer

i think D

anonymous · Answer

When you have a quadratic function in the form:
$a(x-r)(x-s)$
or
$a[k(x-d)]^2+c$
or
$ax^2+bx+c$
Whenever the $a$ co-efficient is negative, it opens downward

anonymous · Answer

Hint:
D can be rewritten as $$-x^2-3$$

anonymous · Answer

@KeithAfasCalcLover so in this case even though it says "check all that apply" only D would be the answer since all the other a coefficients are positive?

anonymous · Answer

Ah-ah-ahh...Be careful Ali, check all of them
The $a$ value for D is $-1$, true. But do any of them have a negative sign around any of the $x^2$s?

anonymous · Answer

In my professional, ahem, (highschool) experience lol I found that when teachers say "check all that apply", its usually because there exist more than one answer

anonymous · Answer

You're very correct! :) So would A and D be the answers since A has a negative in y=2x-x^2?

anonymous · Answer

Bingo :) Haha you're very correct!

That's what I would put.

anonymous · Answer

Thank you so much, you're awesome! :)

anonymous · Answer

Thanks Ali, I try ;) Anytime :)