Put the quadratic into vertex form and state the coordinates of the vertex
y=x^2+8x+12
Vertex form:y=___________
Vertex:(,)
To put the quadratic equation into vertex form, we need to complete the square. The general vertex form of a quadratic equation is given by:
y = a(x-h)^2 + k
where (h,k) represents the coordinates of the vertex.
Let's complete the square for the given equation, y = x^2 + 8x + 12:
y = (x^2 + 8x) + 12
y = (x^2 + 8x + 16) - 16 + 12 (Adding and subtracting (8/2)^2 = 16 to keep the equation balanced)
y = (x + 4)^2 - 4
So the quadratic equation in the vertex form is y = (x + 4)^2 - 4, and the coordinates of the vertex are (-4, -4).