Have I converted correctly from standard form to vertex form?
y = -3x^2 + 12x+1 =
y = -3(x-2)^2 -13
Thanks
Looks to me like you need
-3(x-2)^2 + 13
Oh! I see my error now.
Thank you :)
To determine if you have correctly converted the quadratic equation from standard form to vertex form, you need to understand the properties of the vertex form of a quadratic equation.
The vertex form of a quadratic equation is given by:
y = a(x-h)^2 + k
Where (h, k) represents the coordinates of the vertex.
In standard form, the general equation of a quadratic is:
y = ax^2 + bx + c
To convert from standard form to vertex form, follow these steps:
1. Identify the values of a, b, and c in the standard form equation.
In your equation: y = -3x^2 + 12x + 1, you have:
a = -3
b = 12
c = 1
2. Use the formula to find the x-coordinate of the vertex:
The x-coordinate of the vertex, h, can be calculated using the formula:
h = -b / (2a)
Substituting the values from your equation:
h = -12 / (2*(-3))
h = -12 / (-6)
h = 2
3. Substitute the value of h back into the standard form equation to find the y-coordinate of the vertex.
Substituting h = 2 into the equation:
y = -3(2)^2 + 12(2) + 1
y = -3(4) + 24 + 1
y = -12 + 24 + 1
y = 13
Therefore, the coordinates of the vertex are (2, 13).
Now, let's compare this with your conversion:
The given conversion is: y = -3(x-2)^2 -13
The (h, k) representation of the vertex form is:
y = a(x-h)^2 + k
Comparing this with the given conversion, we can see that the coordinates of the vertex match: (h, k) = (2, 13).
Therefore, your conversion from standard form to vertex form is correct. The correct conversion is:
y = -3(x-2)^2 + 13