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Popular >

range of f(x)=x^2+5x+6

Solution

range

f (x) = x^{2} + 5 x + 6

Solution

f (x) \geq - \frac{1}{4}

+1

Interval Notation

[- \frac{1}{4}, \infty)

Solution steps

Vertex of

x^{2} + 5 x + 6 :

Minimum

(- \frac{5}{2}, - \frac{1}{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{5}{2}, - \frac{1}{4})

f (x) \geq - \frac{1}{4}

Popular Examples

parity f(x)=(7x^4+3x^2+1)/(3x^4-5x-2)parity

f (x) = \frac{7 x ^{4} + 3 x ^{2} + 1}{3 x ^{4} - 5 x - 2}

critical (x^2)/((x-3))critical points

\frac{x ^{2}}{( x - 3 )}

slope ofintercept 8x+3y=24 slope intercept

8 x + 3 y = 24

extreme f(x)=e^4x+e-x extreme points

f (x) = e^{4} x + e - x

simplify (-1.4)(4)simplify

(- 1.4) (4)

Frequently Asked Questions (FAQ)

What is the range of f(x)=x^2+5x+6 ?
The range of f(x)=x^2+5x+6 is f(x)>=-1/4