How do you write the quadratic in vertex form given #y=3x^2-12x+4#?

Answer 1

#y=3(x-2)^2-8#

vertex form is #y=a(x-h)^2 +k#

You must fill in the square with the x terms in order to solve this:

#y=3x^2-12x+4#

first, separate the terms x:

#y - 4=3x^2-12x#
#ax^2 +bx+c# to complete the square #a =1# and #c=(1/2b)^2#

so that a = 1, we must factor out 3:

#y - 4=3(x^2-4x)#

Now add the c to both sides, keeping in mind that since we are removing the right factor, we must multiply the c on the left by three:

#y - 4 +3c=3(x^2-4x +c)#

now figure out c:

#c=(1/2*-4)^2 = 4#

and incorporate it into our formula to finish the square:

#y - 4 +3*4=3(x^2-4x +4)#
#y +8=3(x-2)^2#

At last, separate the y:

#y=3(x-2)^2-8#
given this form we know the vertex is #(-k, h) = (2, -8)# as shown in graph:

plot{y=3x^2-12x+4 [-8.05, 11.95, -8.84, 1.16]}

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To write the quadratic in vertex form given ( y = 3x^2 - 12x + 4 ), follow these steps:

  1. Complete the square for the quadratic expression.
  2. Rewrite the quadratic expression in the form ( a(x - h)^2 + k ), where ( (h, k) ) represents the vertex.

Here's the process:

  1. Complete the square: [ y = 3(x^2 - 4x) + 4 ] [ y = 3(x^2 - 4x + 4 - 4) + 4 ] [ y = 3(x^2 - 4x + 4) - 12 + 4 ] [ y = 3(x - 2)^2 - 8 ]

  2. So, the quadratic in vertex form is: [ y = 3(x - 2)^2 - 8 ]

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7