Question

Hey, just trying to understand the intuition of functions a bit better. f(x) = -5 if x = -2, f(x) = -3x^2 + 4 otherwise. The 4 is the y-intercept, and the -3x squared is the slope, right? Is the -3x squared because the parabola is symmetrical?

Answer 1

You can get the slope by differentiating\[-3x^2 + 4\] to get the slope function as: \[-6x\]

Answer 2

Can you please rephrase your question?

Answer 3

What is the range? but i'd like to know if the 4 is the y-intercept and the -3x^2 is the slope, and if possible can you show me on a graph?

Answer 4

-3x^2 is NOT the slope.

Answer 5

4 is the y-intercept because at x = 0, f(x) = -3(0)^2 + 4 = 4
The slope is -6x, have you use differentiation before?

Answer 6

you can find the slope of the curve by dy/dx. (if you have studied calc)

Answer 7

no not yet, AsianDuck

Answer 8

Ah, i'm just starting calc, that's prob why i don't really get the intuition yet

Answer 9

y = mx + b
here you can apply the logic that "m" is the slope.

but u have a quadratic equation here. where the slope will change on every step.

Answer 10

can you please explain differentiation?

Answer 11

http://www.youtube.com/watch?v=rAof9Ld5sOg

Answer 12

but if f(x) = -3x^2 + 4 (wouldn't that count as y = mx + b) with the -3x being the slope??

Answer 13

you have a QUADRATIC EQUATION sir.
with "x^2"

whereas in linear equation there is "NO x^2" there's only "x"

Answer 14

ah okay :D thank you

Answer 15

any more confusions?

i can feel the happiness.