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Popular >

range of f(x)=-1/2 x^2+7x-3

Solution

range

f (x) = - \frac{1}{2} x^{2} + 7 x - 3

Solution

f (x) \leq \frac{43}{2}

+1

Interval Notation

(- \infty, \frac{43}{2}]

Solution steps

Vertex of

- \frac{1}{2} x^{2} + 7 x - 3 :

Maximum

(7, \frac{43}{2})

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 = - \frac{1}{2},

Vertex

(x_{v}, y_{v}) = (7, \frac{43}{2})

f (x) \leq \frac{43}{2}

Popular Examples

domain of f(x)= 3/(x-2)domain

f (x) = \frac{3}{x - 2}

intercepts of f(x)=\sqrt[3]{x+1}intercepts

parity sin(x)parity

sin (x)

critical e^{3x}(2-x)critical points

e^{3 x} (2 - x)

f (a) = a^{2}

Frequently Asked Questions (FAQ)

What is the range of f(x)=-1/2 x^2+7x-3 ?
The range of f(x)=-1/2 x^2+7x-3 is f(x)<= 43/2