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Popular >

range of 3x-x^2

Solution

range

3 x - x^{2}

Solution

f (x) \leq \frac{9}{4}

+1

Interval Notation

(- \infty, \frac{9}{4}]

Solution steps

Vertex of

3 x - x^{2} :

Maximum

(\frac{3}{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{3}{2}, \frac{9}{4})

f (x) \leq \frac{9}{4}

Popular Examples

domain of 1/(4x-8)domain

\frac{1}{4 x - 8}

domain of-1/2 sqrt(x+3)domain

- \frac{1}{2} x + 3

parity f(x)=-x^2-x-1 parity

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

domain of 1/4 x-1/2 domain

\frac{1}{4} x - \frac{1}{2}

intercepts of f(x)=2x+y=10 intercepts

f (x) = 2 x + y = 10

Frequently Asked Questions (FAQ)

What is the range of 3x-x^2 ?
The range of 3x-x^2 is f(x)<= 9/4