Question

1. $y=(x^2 - 8x) - 10$

Explanation:

Assuming we want to rewrite the quadratic function in vertex form (completing the square), here's the step - by - step solution:

Step 1: Complete the square for the quadratic part

For the quadratic expression \(x^{2}-8x\), we use the formula for completing the square. The coefficient of \(x\) is \(- 8\). To complete the square, we take half of \(-8\), which is \(\frac{-8}{2}=-4\), and then square it: \((-4)^{2} = 16\). We add and subtract 16 inside the parentheses.
\(y=(x^{2}-8x + 16-16)-10\)

Step 2: Rewrite the perfect square trinomial

The expression \(x^{2}-8x + 16\) is a perfect square trinomial and can be written as \((x - 4)^{2}\). So we have:
\(y=((x - 4)^{2}-16)-10\)

Step 3: Simplify the expression

We simplify the constants:
\(y=(x - 4)^{2}-16 - 10\)
\(y=(x - 4)^{2}-26\)

Answer:

In vertex form, \(y=(x - 4)^{2}-26\)