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Popular >

range of x^2-7x-30

Solution

range

x^{2} - 7 x - 30

Solution

f (x) \geq - \frac{169}{4}

+1

Interval Notation

[- \frac{169}{4}, \infty)

Solution steps

Vertex of

x^{2} - 7 x - 30 :

Minimum

(\frac{7}{2}, - \frac{169}{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{7}{2}, - \frac{169}{4})

f (x) \geq - \frac{169}{4}

Popular Examples

monotone f(x)=sqrt(x^2-1)monotone intervals

f (x) = x^{2} - 1

domain of f(x)=(2x+8)/(x^2-3x-18)domain

f (x) = \frac{2 x + 8}{x ^{2} - 3 x - 18}

domain of f(x)= 5/(2sqrt(4+5x))domain

f (x) = \frac{5}{2 4 + 5 x}

shift 2cos(3x+pi/2)shift

2 cos (3 x + \frac{π}{2})

domain of f(x)=((x-2))/((1-3x))domain

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

Frequently Asked Questions (FAQ)

What is the range of x^2-7x-30 ?
The range of x^2-7x-30 is f(x)>=-169/4