transform y=x²-2x-4 ​

Step-by-step explanation:To transform the equation \( y = x^2 - 2x - 4 \) into vertex form, we can complete the square. Here’s how it’s done step by step:1. **Start with the original equation:** \[ y = x^2 - 2x - 4 \]2. **Group the \( x \) terms:** \[ y = (x^2 - 2x) - 4 \]3. **Complete the square for the expression in the parentheses:** - Take the coefficient of \( x \) (which is -2), divide by 2, and square it: \[ \left( \frac{-2}{2} \right)^2 = 1 \]4. **Add and subtract this square inside the parentheses:** \[ y = (x^2 - 2x + 1 - 1) - 4 \] \[ y = ((x - 1)^2 - 1) - 4 \]5. **Simplify the equation:** \[ y = (x - 1)^2 - 5 \]Now the equation in vertex form is:\[y = (x - 1)^2 - 5\]The vertex of the parabola described by this equation is at the point (1, -5). If you need further assistance or have other questions, feel free to ask!

Answered by romnickpallon | 2024-09-04