Y = - X^2 + X + 6
set to 0
- X^2 + X + 6
I always multiply through by - 1. Different direction graph, but same 0's
-1(-X^2 + X + 6 = 0)
X^2 - X - 6 = 0
what two factors of - 6 add up to - 1 ?
(X - 3)(X + 2)
----------------------Now,
X = 3
X = -2
As functions zeros
the zeros of a function is/are the values of the variables in the function that makes/make the function zero. for example: In f(x) = x2 -7x + 10, the zeros of the function are 2 and 5 because these will make the function zero.
That is not a function, although it does involve the function of addition. A function is something that is done to numbers.
Interpreting that function as y=x2+2x+1, the graph of this function would be a parabola that opens upward. It would be equivalent to y=(x+1)2. Its vertex would be at (-1,0) and this vertex would be the parabola's only zero.
It keeps the same shape and size, but the whole thing rises four units on the paper, as if by magic.
1 and 2
No, it is not.
Yes
Yes. Think of y as being a function of x. y = f(x) = x2 + 1
Implicit: x2 + 2y = 5 Explicit : y = (5 - x2)/2
x2 + x2 = 2x2
x^2 + 11x + 6 has no rational zeros.
(the shape is an upside down 'u').
x = -3y = -14
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
the zeros of a function is/are the values of the variables in the function that makes/make the function zero. for example: In f(x) = x2 -7x + 10, the zeros of the function are 2 and 5 because these will make the function zero.
x3 + x2 - 17x + 15 = (x - 1)(x - 3)(x + 5). Thus, the zeros are 1, 3, and -5. All three zeros are rational.
0