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Popular >

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

Solution

range

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

Solution

f (x) \geq - \frac{41}{4}

+1

Interval Notation

[- \frac{41}{4}, \infty)

Solution steps

Vertex of

x^{2} + x - 10 :

Minimum

(- \frac{1}{2}, - \frac{41}{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{41}{4})

f (x) \geq - \frac{41}{4}

Popular Examples

parity sin(tan(3x))parity

sin (tan (3 x))

midpoint (0,-5),(4,3)midpoint

(0, - 5), (4, 3)

slope of x=8y slope

x = 8 y

inverse of f(x)=(x^2-5)/(7x^2)inverse

f (x) = \frac{x ^{2} - 5}{7 x ^{2}}

critical f(x)= 1/(x^2+1)critical points

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

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2+x-10 ?
The range of f(x)=x^2+x-10 is f(x)>=-41/4