1. **State the problem:** Convert each quadratic equation from vertex form to standard form. 2. **Recall the vertex form:** $$y = a(x-h)^2 + k$$ where $(h,k)$ is the vertex. 3. **Standard form:** $$y = ax^2 + bx + c$$ 4. **Method:** Expand the squared term and simplify. --- **Problem 1:** $$y = (x + 3)^2 - 6$$ Expand: $$y = (x + 3)(x + 3) - 6 = x^2 + 3x + 3x + 9 - 6$$ Simplify: $$y = x^2 + 6x + 3$$ --- **Problem 2:** $$y = 2(x - 7)^2 - 4$$ Expand inside the square: $$y = 2(x^2 - 14x + 49) - 4$$ Distribute 2: $$y = 2x^2 - 28x + 98 - 4$$ Simplify: $$y = 2x^2 - 28x + 94$$ --- **Problem 3:** $$y = -9(x + 9)^2 - 2$$ Expand: $$y = -9(x^2 + 18x + 81) - 2$$ Distribute -9: $$y = -9x^2 - 162x - 729 - 2$$ Simplify: $$y = -9x^2 - 162x - 731$$ --- **Problem 4:** $$y = (x + 5)^2 + 8$$ Expand: $$y = x^2 + 10x + 25 + 8$$ Simplify: $$y = x^2 + 10x + 33$$ --- **Final answers:** 1. $$y = x^2 + 6x + 3$$ 2. $$y = 2x^2 - 28x + 94$$ 3. $$y = -9x^2 - 162x - 731$$ 4. $$y = x^2 + 10x + 33$$