Complete the square to re-write the quadratic function in vertex form:

Question

y, equals, minus, 8, x, squared, minus, 96, x, minus, 289
y=−8x2 −96x−289

Answer 1

To complete the square, we want to rearrange the quadratic function to have the form: y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

We start by factoring out the common factor of -8 from the x^2 and x terms:
y = -8(x^2 + 12x) - 289

Next, we need to determine what number to add and subtract inside the parentheses to complete the square. The number we need to add and subtract is found by taking half of the coefficient of x and squaring it. In this case, we take half of 12 (which is 6) and square it (which gives us 36).
y = -8(x^2 + 12x + 36 - 36) - 289

Now we can rewrite the expression as:
y = -8[(x + 6)^2 - 36] - 289

Simplifying inside the brackets:
y = -8(x + 6)^2 + 288 - 289

Combine like terms:
y = -8(x + 6)^2 - 1

Therefore, the quadratic function rewritten in vertex form is:
y = -8(x + 6)^2 - 1