Question

Find the minimum or maximum value of the function. Describe the domain and range of the function and where the function in decreasing or increasing:

y=6x^2-1

I'm not sure how to figure out how to find the x and y values because its not already in standard form for me to find the vertex? What am I doing wrong?

Answer 1

Vertex form is: y - k = a(x - h)^2 where (h,k) is the vertex.
Rearrange y = 6x^2 - 1 to look like the equation above.
y + 1 = 6(x - 0)^2
what is (h, k)?

Answer 2

y + 1 = 6(x - 0)^2
y - (-1) = 6(x - 0)^2
y - k = a(x - h)^2
What is (h, k) ?

Answer 3

If you are not familiar with the vertex form of a parabola you can skip the above method and calculate the x-coordinate of the vertex from the standard form of a parabola.
For y = ax^2 + bx + c
The x-coordinate of the vertex is -b/(2a)

Here y = 6x^2 - 1 which can be written as follows:
y = 6x^2 + 0x - 1
where a = 6, b = 0, c = -1
The x-coordinate of the vertex is -b/(2a) = -0/(2*6) = 0
put x = 0 and find y: y = 0 + 0 - 1 = -1
Vertex is at (0, -1)