Question

Explain the steps to finding the vertex of g(x) = 3x2 + 12x + 15

Answer 1

Vertex: (-2, 3)

Explanation:

We first have to find the x - variable of the vertex point.

The formula to find the x - variable is x = -b/ 2a.

`3x^(2) + 12x + 15`

a b c

Substitute the values into the formula.

x = - 12 / 2(3)

x = - 12 / 6

x = - 2 < - This is the x - variable

Now we have to find the y - variable of the vertex point.

To find the y - variable, we have to substitute the x value into the original equation (
`3x^(2) + 12x + 15`).

g(x) = y

`y = 3(-2)^(2) + 12(-2) + 15\\`

`y = 3(4) - 24 + 15`

`y = 12 - 24 + 15`

`y = - 12 + 15`

`y = 3`

So, now that we have the x and y values, we can find the vertex which is (-2, 3).

Hope this helps!