SOLUTION: Find the vertex of y=3x^2+18x+24

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Question 1207030: Find the vertex of y=3x^2+18x+24
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=3%28x%5E2%2B6x%2B8%29
y=3%28x%5E2%2B6x%2B9-9%2B8%29
y=3%28%28x%2B3%29%5E2-1%29
y=3%28x%2B3%29%5E2-3

Vertex is read directly from the equation in this form.
(-3,-3)

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: (-3, -3)

Explanation

Compare y=3x^2+18x+24 to the template y = ax^2+bx+c
a = 3
b = 18
c = 24

The vertex is located at (h,k)
Let's determine the x coordinate of the vertex.
h = -b/(2a)
h = -18/(2*3)
h = -3

Plug this into the equation to find the y coordinate of the vertex.
y = 3x^2+18x+24
y = 3*(-3)^2+18(-3)+24
y = -3

The vertex is located at (h,k) = (-3, -3)

We go from vertex form
y = a(x-h)^2 + k
to
y = 3(x-(-3))^2 + (-3)
y = 3(x + 3)^2 - 3