How do you write the quadratic in vertex form given #y=3x^2-12x+4#?
You must fill in the square with the x terms in order to solve this:
first, separate the terms x:
so that a = 1, we must factor out 3:
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:
now figure out c:
and incorporate it into our formula to finish the square:
At last, separate the y:
plot{y=3x^2-12x+4 [-8.05, 11.95, -8.84, 1.16]}
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To write the quadratic in vertex form given ( y = 3x^2 - 12x + 4 ), follow these steps:
- Complete the square for the quadratic expression.
- Rewrite the quadratic expression in the form ( a(x - h)^2 + k ), where ( (h, k) ) represents the vertex.
Here's the process:
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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 ]
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So, the quadratic in vertex form is: [ y = 3(x - 2)^2 - 8 ]
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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.
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