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Popular >

range of x^2+3x+1

Solution

range

x^{2} + 3 x + 1

Solution

f (x) \geq - \frac{5}{4}

+1

Interval Notation

Solution steps

Vertex of

x^{2} + 3 x + 1 :

Minimum

(- \frac{3}{2}, - \frac{5}{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{5}{4})

f (x) \geq - \frac{5}{4}

Graph

Popular Examples

intercepts of (x^2-9x)/(x+3)intercepts

\frac{x ^{2} - 9 x}{x + 3}

extreme f(x)=-8x^3+24x+7 extreme points

f (x) = - 8 x^{3} + 24 x + 7

inverse of f(x)=sqrt(x^2+8x)inverse

f (x) = x^{2} + 8 x

inverse of f(x)=5(x+4)^2-1 inverse

f (x) = 5 (x + 4)^{2} - 1

slope of y=7-4x slope

y = 7 - 4 x

Frequently Asked Questions (FAQ)

What is the range of x^2+3x+1 ?
The range of x^2+3x+1 is f(x)>=-5/4