1. **Problem Statement:** We are given the quadratic function $$f(x) = x^2 - 14x + 48$$ and need to describe its graph by identifying key features such as intercepts, direction of opening, and axis of symmetry. 2. **Formula and Rules:** - The quadratic function is in standard form $$ax^2 + bx + c$$ where $$a=1$$, $$b=-14$$, and $$c=48$$. - The parabola opens upward if $$a > 0$$ and downward if $$a < 0$$. - The axis of symmetry is given by $$x = -\frac{b}{2a}$$. - The vertex is at $$\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$. - The y-intercept is at $$f(0) = c$$. - The x-intercepts (roots) are found by solving $$f(x) = 0$$. 3. **Calculate the y-intercept:** $$f(0) = 0^2 - 14 \times 0 + 48 = 48$$ So, the y-intercept is at $$(0, 48)$$. 4. **Determine the direction of the parabola:** Since $$a = 1 > 0$$, the parabola opens **upward**. 5. **Find the axis of symmetry:** $$x = -\frac{b}{2a} = -\frac{-14}{2 \times 1} = \frac{14}{2} = 7$$ So, the axis of symmetry is $$x = 7$$. 6. **Find the x-intercepts:** Solve $$x^2 - 14x + 48 = 0$$. Factor the quadratic: $$x^2 - 14x + 48 = (x - 6)(x - 8) = 0$$ So, $$x = 6$$ or $$x = 8$$. The x-intercepts are $$(6, 0)$$ and $$(8, 0)$$. 7. **Summary of graph features:** - y-intercept: $$(0, 48)$$ - Parabola opens upward - x-intercepts: $$(6, 0)$$ and $$(8, 0)$$ - Axis of symmetry: $$x = 7$$ **Note:** The statement "The parabola opens downward" and "The axis of symmetry is x=6" are incorrect based on calculations. **Final answer:** - The y-intercept is $$(0, 48)$$. - The parabola opens upward. - The x-intercepts are $$(6, 0)$$ and $$(8, 0)$$. - The axis of symmetry is $$x = 7$$.