Question

Find the minimum or maximum of the function. Describe the domain/range in interval notation y=6x^2-1

Answer 1

max is at vertex

in form $y=ax^2+bx+c$

the x value of the vertex is $\frac{-b}{2a}$

given, $y=6x^2-1$

a=6, b=0

the x value of the vertex is -0/(2*6)=0

the y value is $y=6(0)^2-1=0-1=-1$

so vertex is at (0,-1)

since the value of a is positive, the parabola opens up and the vertex is a minimum value of the function

therefore that value is the smallest value the function can be

domain=numbesr you can use for x

range=numbesr you get out of inputting the domain

domain=all real numbers

range is {y | y≥-1} since y=-1 is the minimum