so I sent it this:
write "((-2x)^(2))+(8x)-(3)" in vertex form
and then it gave me this image (with all the red text) and then i hovered over the red text and it gave me this image which looks like an error code
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so I sent it this:
write "((-2x)^(2))+(8x)-(3)" in vertex form
and then it gave me this image (with all the red text) and then i hovered over the red text and it gave me this image which looks like an error code
Here's what gpt-3.5 said:
To express the quadratic function (f(x) = (-2x)^2 + 8x - 3) in vertex form, we can complete the square. The vertex form of a quadratic function is given by:
[f(x) = a(x - h)^2 + k]
To complete the square, we focus on the quadratic terms and the linear term.
Starting with the given function:
[f(x) = (-2x)^2 + 8x - 3]
To complete the square, we need to add and subtract ((2/2)^2 = 1) inside the parenthesis:
[4(x^2 + 2x + 1 - 1)]
Now, the function in vertex form is (f(x) = 4(x + 1)^2 - 4 - 3).
Simplifying further, we get:
[f(x) = 4(x + 1)^2 - 7]
So, the given quadratic function in vertex form is (f(x) = 4(x + 1)^2 - 7).
here it is again, but in markdown: