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Popular >

range of y=x^2-4x+7

Solution

range

y = x^{2} - 4 x + 7

Solution

f (x) \geq 3

+1

Interval Notation

[3, \infty)

Solution steps

Vertex of

x^{2} - 4 x + 7 :

Minimum

(2, 3)

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}) = (2, 3)

f (x) \geq 3

Popular Examples

extreme x^2-6x extreme points

x^{2} - 6 x

asymptotes of f(x)= 2/(3x(x-1)(x+5))asymptotes

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

monotone f(x)=-14x^2-16x+128 monotone intervals

f (x) = - 14 x^{2} - 16 x + 128

critical f(x)=x^{2/3}critical points

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

perpendicular y=3x+2,(3,5)perpendicular

y = 3 x + 2, (3, 5)

Frequently Asked Questions (FAQ)

What is the range of y=x^2-4x+7 ?
The range of y=x^2-4x+7 is f(x)>= 3