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Popular >

range of 3x^2-5x+7

Solution

range

3 x^{2} - 5 x + 7

Solution

f (x) \geq \frac{59}{12}

+1

Interval Notation

[\frac{59}{12}, \infty)

Solution steps

Vertex of

3 x^{2} - 5 x + 7 :

Minimum

(\frac{5}{6}, \frac{59}{12})

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 = 3,

Vertex

(x_{v}, y_{v}) = (\frac{5}{6}, \frac{59}{12})

f (x) \geq \frac{59}{12}

Popular Examples

parity tan^2(x)parity

tan^{2} (x)

domain of (2x^2+2)^3(x^2-1)^2 domain

(2 x^{2} + 2)^{3} (x^{2} - 1)^{2}

domain of f(x)=(\sqrt[3]{x^5+3x-3})/(3x-2)domain

domain of log_{10}(2-x)domain

lo g_{10} (2 - x)

midpoint (-1,2),(-1,-4)midpoint

(- 1, 2), (- 1, - 4)

Frequently Asked Questions (FAQ)

What is the range of 3x^2-5x+7 ?
The range of 3x^2-5x+7 is f(x)>= 59/12