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Popular >

range of f(x)=-x^2+9x+10

Solution

range

f (x) = - x^{2} + 9 x + 10

Solution

f (x) \leq \frac{121}{4}

+1

Interval Notation

(- \infty, \frac{121}{4}]

Solution steps

Vertex of

- x^{2} + 9 x + 10 :

Maximum

(\frac{9}{2}, \frac{121}{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{9}{2}, \frac{121}{4})

f (x) \leq \frac{121}{4}

Popular Examples

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4 y - 1 = - 3 (4 - 2 x)

domain of f(x)=(2x)/(2x^2+3x-20)domain

f (x) = \frac{2 x}{2 x ^{2} + 3 x - 20}

domain of f(x)=tan((pix)/2)domain

f (x) = tan (\frac{π x}{2})

inverse of f(x)=(6x-1)/(2x+3)inverse

f (x) = \frac{6 x - 1}{2 x + 3}

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

f (x) = 2 - x - 3

Frequently Asked Questions (FAQ)

What is the range of f(x)=-x^2+9x+10 ?
The range of f(x)=-x^2+9x+10 is f(x)<= 121/4