What is the vertex form of y = 3x^2 – 12x + 5
I would like some help on how to solve this problem in steps.
Thanks!
Thanks! This really helped!
May I have your help on two more problems?
To convert the given quadratic equation into vertex form, which is in the form y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex, follow these steps:
Step 1: Identify the coefficients in the original equation.
In y = 3x^2 – 12x + 5:
- Coefficient 'a' is 3
- Coefficient 'b' is -12
- Coefficient 'c' is 5
Step 2: Find the x-coordinate of the vertex.
Use the formula x = -b / 2a to find the x-coordinate of the vertex. Substitute the values of coefficients 'a' and 'b' into the formula:
x = -(-12) / (2 * 3)
x = 12 / 6
x = 2
Step 3: Substitute the x-coordinate of the vertex into the original equation to find the y-coordinate.
Substitute x = 2 into the original equation:
y = 3(2)^2 – 12(2) + 5
y = 12 – 24 + 5
y = -7
Step 4: Write the equation in vertex form.
Now that we have the x-coordinate (2) and y-coordinate (-7) of the vertex, we can write the equation in vertex form:
y = 3(x - 2)^2 - 7
Therefore, the vertex form of y = 3x^2 – 12x + 5 is y = 3(x - 2)^2 - 7.
3x^2 - 12x + 5
3(x^2 - 4x) + 5
now add and subtract 3*4
3(x^2-4x+4) + 5 - 12
3(x-2)^2 - 7