Question

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

Answer 1

Answer:

Vertex: (-2, 3)

Step-by-step 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!