1. **Problem statement:** Sketch the graph of the quadratic function $$y = - (x-1)(x+6)$$. 2. **Formula and rules:** This is a quadratic function in factored form. The x-intercepts are found by setting $$y=0$$ and solving for $$x$$. 3. **Find x-intercepts:** $$0 = - (x-1)(x+6)$$ Removing the negative sign for solving zeros: $$0 = (x-1)(x+6)$$ Set each factor to zero: $$x-1=0 \Rightarrow x=1$$ $$x+6=0 \Rightarrow x=-6$$ So, the x-intercepts are at points $$(1,0)$$ and $$(-6,0)$$. 4. **Find y-intercept:** Set $$x=0$$: $$y = - (0-1)(0+6) = - (-1)(6) = 6$$ So, the y-intercept is at $$(0,6)$$. 5. **Find turning point (vertex):** The vertex lies midway between the x-intercepts: $$x = \frac{1 + (-6)}{2} = \frac{-5}{2} = -2.5$$ Calculate $$y$$ at $$x=-2.5$$: $$y = - (-2.5 - 1)(-2.5 + 6) = - (-3.5)(3.5) = - (-12.25) = 12.25$$ So, the turning point is at $$(-2.5, 12.25)$$. 6. **Graph features:** - The parabola opens downward (due to the negative sign). - It crosses the x-axis at $$(1,0)$$ and $$(-6,0)$$. - It crosses the y-axis at $$(0,6)$$. - The vertex is a maximum point at $$(-2.5, 12.25)$$. Final answer: The graph of $$y = - (x-1)(x+6)$$ has x-intercepts at $$(1,0)$$ and $$(-6,0)$$, y-intercept at $$(0,6)$$, and a maximum turning point at $$(-2.5, 12.25)$$.