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Popular >

range of x^2-x-6

Solution

range

x^{2} - x - 6

Solution

f (x) \geq - \frac{25}{4}

+1

Interval Notation

[- \frac{25}{4}, \infty)

Solution steps

Vertex of

x^{2} - x - 6 :

Minimum

(\frac{1}{2}, - \frac{25}{4})

For a parabola

a x^{2} + b x + c

with Vertex

(x_{v}, y_{v})

If

a < 0

the range is

f (x) \leq y_{v}

If

a > 0

the range is

f (x) \geq y_{v}

a = 1,

Vertex

(x_{v}, y_{v}) = (\frac{1}{2}, - \frac{25}{4})

f (x) \geq - \frac{25}{4}

Popular Examples

critical f(x)=(x-1)/(x^2-x+1)critical points

f (x) = \frac{x - 1}{x ^{2} - x + 1}

domain of f(x)=(2x^3-5)/(x^2+x-6)domain

f (x) = \frac{2 x ^{3} - 5}{x ^{2} + x - 6}

slope of y= 4/5 x+2 slope

y = \frac{4}{5} x + 2

domain of g(x)=|x|+13 domain

g (x) = ∣ x ∣ + 13

inverse of f(x)=y inverse

f (x) = y

Frequently Asked Questions (FAQ)

What is the range of x^2-x-6 ?
The range of x^2-x-6 is f(x)>=-25/4