Graphing Quadratic Equation?

Question

Ok, the probem is f(x) < -x^2. I know that the graph's vertex will be it's highest points, and it will look like a sad face, to put it simply. Because there's no B, that gives me X=0, which then sticks me with Y=0. So, I presume my vertex is on (0,0). I know I need to substitute to find Y, but I have no Y, so I'm kind of stuck. :/ Any help?

I understand that f(x)=y, since I have no B or C, if I adhere to the technical formula. But, I need to shade in, so how do I make the graph to shade? That's where I'm stuck.

Answer 1

You are right about (0,0) being the vertex.
Draw out your graph just as if you had y = - x^2, but use a broken line to indicate the inequality (that's the first value y CANNOT have) Then simply shade inside the parabola, giving you a sad face with a long beard.

Answer 2

Yes, the answer is that f(x) is just another way of saying "y". It's a bit more precise, since f(x) refers to those equations which are actually functions--and a function is defined as an expression which has a value of y for every value of x over which it's being evaluated. That is, something like y=1/x isn't a function for all possible values of x, because at x=0 the value for y is undefined. However, something like y=x^2 *is* a function since for any value of x you can find the value for y; hence, it's legitimate to write
f(x) = x^2.

You may see f(x) = 1/x, even if it's not truly a function, but just think of it as y=1/x anyway.

Answer 3

Ok, since you want all values below the parabola since it is "less than," shade the region beneath (inside) the "sad face."

Your graph will look like an upside down parabola (or sad face) shaded below the frown.

Answer 4

to figure out which bit to shade i pick a point inside the parabola eg(0,-1) and a point outside of it eg (1,1) and sub them into the equation

Answer 5

the answer is i dont know, i struggled with this exept for the Quadratic formula all year, im just as stuck as you, you still have school

Answer 6

f(x) = y

really