Question

Given the function f(x) = x2 and k = –1, which of the following represents a function opening downward?

f(x) + k
kf(x)
f(x + k)
f(kx)

Answer 1

the function is a quadratic, parabola f(x) = a*x^2 + b*x + c

here a=1, and b and c are zero

Answer 2

If you recall, the 'a' coefficient on the x^2 term can tell you which way the parabola opens, up+ or down -

Answer 3

the thing starts opening upwards f(x) = x^2

to open down, need a negative in the front

Answer 4

so to do that change using that k=-1

you can multiply f(x) by that k

Answer 5

k*f(x) = (-1)*f(x) = (-1)*x^2

Answer 6

so the answer would be b?

Answer 7

f(x) + k --- that shifts the whole graph up/down by k, any value is just increased by k

k*f(x) --- scale, also changed the opening direction depending on the sign of 'a'

f(x + k) -- horizontal shifts , f(x-a) , so f(x+k) moves left k units for the whole graph

Answer 8

if I’m being honest, I’m not sure what that means. What would the answer be, or could you try showing me. @DanJS

Answer 9

@DanJS

Answer 10

was gone for awhile,

yeah for f(x) = x^2, which is a parabola with vertex at the origin and opening upwards,

to flip it to open down, you need a negative value as a coefficient to x^2

Answer 11

yeah, k*f(x) = -x^2

opens down now

Answer 12

I just figured you probably may of went over the other ideas in the answer choices, i was typing them to show why wrong,