0
y = -x2 + 1
This function describes a parabola that opens downward. To find the top of it's range, you need to find it's focal point. You can do that very easily by taking the derivative of the equation and solving it for 0:
y = -x2 + 1
∴ y' = -2x
let y' = 0:
0 = -2x
∴ x = 0
Now you can calculate the y value at that point:
y = -02 + 1
∴ y = 1
So that function describes an upside down parabola whose peak is at the point {0, 1}. It's range then is:
{y | y ∈ ℜ, y ≤ 1}
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What is the range of the function y equals x2 plus 1?
The answer depends on the domain. If the domain is the whole of the real numbers, the range in y ≥ 1. However, you can choose to have the domain as [1, 2] in which case the range will be [2, 5]. If you choose another domain you will get another range.
X2 plus 7 equals 36?
if x2 + 7 = 37, then x2 = 29 and x = ±√29
Y equals x2 plus 2x plus 1?
y = x2 + 2x + 1zeros are:0 = x2 + 2x + 10 = (x + 1)(x + 1)0 = (x + 1)2x = -1So that the graph of the function y = x + 2x + 1 touches the x-axis at x = -1.
What is the discriminant of x2 plus 3x plus 8 equals 0?
The discriminant formula. b2 - 4ac 32 - 4(1)(8) 9 - 32 = - 23 ===========This shows no real roots to this function.
What is the value of the function x2 plus 3 at x equals 5?
f(x) = x2 + 3 ----> f(5) = (5)2 + 3 ----> f(5) = 28
