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.
[tex]3x^{2} + 12x + 15[/tex]
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 ([tex]3x^{2} + 12x + 15[/tex]).
g(x) = y
[tex]y = 3(-2)^{2} + 12(-2) + 15\\[/tex]
[tex]y = 3(4) - 24 + 15[/tex]
[tex]y = 12 - 24 + 15[/tex]
[tex]y = - 12 + 15[/tex]
[tex]y = 3[/tex]
So, now that we have the x and y values, we can find the vertex which is (-2, 3).
Hope this helps!
