Question

Please help me with this, #5 was- Please write the following function in the form y- k = a(x-h)^2

y= x^2-4x+3
And I got y-2=1(x-2)^2

Answer 1

To rewrite the function y = x^2 - 4x + 3 in the form y - k = a(x - h)^2, we need to complete the square. Here's how we can do it:

y = x^2 - 4x + 3

First, we need to find the value of h by taking half of the coefficient of x and squaring it. In this case, h = (-4/2)^2 = (-2)^2 = 4.

Next, we subtract and add 4 within the parentheses:

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

Now, we can rewrite the expression within the parentheses as a perfect square:

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

Simplifying further:

y = (x - 2)^2 - 1

Finally, we can compare this expression with the desired form y - k = a(x - h)^2:

y - 1 = 1(x - 2)^2

Therefore, the function y = x^2 - 4x + 3 can be written as y - 1 = 1(x - 2)^2.