1. **State the problem:** We are given the quadratic expression $$(x-2)(x+4)$$ and need to find its vertex and y-intercept without graphing. 2. **Expand the expression:** Use the distributive property (FOIL) to expand: $$ (x-2)(x+4) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8 $$ 3. **Find the y-intercept:** The y-intercept occurs when $x=0$. Substitute $x=0$: $$ y = 0^2 + 2(0) - 8 = -8 $$ So, the y-intercept is at the point $$(0, -8)$$. 4. **Convert the quadratic to vertex form:** The vertex form is $$y = a(x-h)^2 + k$$, where $$(h,k)$$ is the vertex. We use completing the square: $$ y = x^2 + 2x - 8 $$ Take the coefficient of $x$, which is 2, divide by 2 and square it: $$ \left(\frac{2}{2}\right)^2 = 1 $$ Add and subtract 1 inside the equation: $$ y = (x^2 + 2x + 1) - 1 - 8 = (x+1)^2 - 9 $$ 5. **Identify the vertex:** From vertex form $$ y = (x+1)^2 - 9 $$ The vertex is $$(-1, -9)$$. **Final answers:** - Vertex: $$(-1, -9)$$ - Y-intercept: $$(0, -8)$$