Find the minimum or maximum of the function. Describe the domain/range in interval notation y=6x^2-1
1 answer:
max is at vertex
in form
the x value of the vertex is
given,
a=6, b=0
the x value of the vertex is -0/(2*6)=0
the y value is
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
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You need these two basic solutions and facts to find the equation of a line:
- If you know the gradient
and one point
:
- If you know the gradient two points
:
- The slope of a line is the coefficient m when you write it in the
form
- Parallel lines have the same slope
- The slopes of perpendicular lines give -1 when multiplied
We can use this list to solve all the exercises:
b)
Use the first equation to get
c)
Use the second equation to get
d) same as c)
e) We derive the slope of the line by writing it as
So, the slope is -1/5. From here, it's the same as b)
f) same as e)
g) Again we find the slope as
so the slope is -3, and a perpendicular line has slope 1/3. From there, it's the same as b).