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 the 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 y-intercept is the value of $$f(0) = c$$. - The x-intercepts (roots) are found by solving $$f(x) = 0$$. 3. **Find the y-intercept:** - Substitute $$x=0$$ into the function: $$f(0) = 0^2 - 14 \times 0 + 48 = 48$$ - 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 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 $$(8,0)$$. 6. **Find the axis of symmetry:** - Use the formula: $$x = -\frac{b}{2a} = -\frac{-14}{2 \times 1} = \frac{14}{2} = 7$$ - The axis of symmetry is $$x = 7$$. **Summary:** - The y-intercept is $$(0,48)$$. - The parabola opens **upward**. - The x-intercepts are $$(6,0)$$ and $$(8,0)$$. - The axis of symmetry is $$x = 7$$. **Note:** The statement "The parabola opens downward" and "The axis of symmetry is x=6" are incorrect based on the 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 $$x=7$$.