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Popular >

range of x^2+x-2

Solution

range

x^{2} + x - 2

Solution

f (x) \geq - \frac{9}{4}

+1

Interval Notation

[- \frac{9}{4}, \infty)

Solution steps

Vertex of

x^{2} + x - 2 :

Minimum

(- \frac{1}{2}, - \frac{9}{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{9}{4})

f (x) \geq - \frac{9}{4}

Popular Examples

domain of 1/(\sqrt[4]{x^2-3x)}domain

intercepts of (x+1)/(2x-1)intercepts

\frac{x + 1}{2 x - 1}

inverse of f(x)=(x-1)^2-6 inverse

f (x) = (x - 1)^{2} - 6

domain of f(x)=(6x)/(sqrt(x+5))domain

f (x) = \frac{6 x}{x + 5}

inflection f(x)=2x(x+4)^2 inflection points

f (x) = 2 x (x + 4)^{2}

Frequently Asked Questions (FAQ)

What is the range of x^2+x-2 ?
The range of x^2+x-2 is f(x)>=-9/4