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Popular Functions >

range of f(x)=x^2-3x-4

Solution

range

f (x) = x^{2} - 3 x - 4

Solution

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

+1

Interval Notation

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

Solution steps

Vertex of

x^{2} - 3 x - 4 :

Minimum

(\frac{3}{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{3}{2}, - \frac{25}{4})

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

Graph

Popular Examples

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critical f(x)=1

extreme f(x)=(3x)/(9-x^2)

inverse of f(x)=(x+5)^2-2

extreme f(x)=3xsqrt(5-x)

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2-3x-4 ?
The range of f(x)=x^2-3x-4 is f(x)>=-25/4