1. The topic is analyzing algebraic functions, which involves understanding properties like intercepts, extrema, domain, and range. 2. A beginner-level question could be: Analyze the function $$f(x) = x^2 - 4x + 3$$. 3. Step 1: State the problem clearly: Find the intercepts, vertex (extremum), and determine the shape of the parabola represented by the function. 4. Step 2: Find the y-intercept by setting $$x=0$$: $$f(0) = 0^2 - 4\cdot0 + 3 = 3$$, so the y-intercept is $(0,3)$. 5. Step 3: Find the x-intercepts by solving $$f(x) = 0$$: $$x^2 - 4x + 3 = 0$$ Factor: $$(x-3)(x-1) = 0$$ So, $$x=3$$ or $$x=1$$, giving x-intercepts at $(3,0)$ and $(1,0)$. 6. Step 4: Find the vertex (extremum). The vertex of a parabola $$ax^2 + bx + c$$ is at $$x = -\frac{b}{2a}$$. Here, $$a=1$$, $$b=-4$$, so $$x = -\frac{-4}{2 \cdot 1} = 2$$. Find $$f(2)$$: $$f(2) = 2^2 - 4\cdot2 + 3 = 4 -8 +3 = -1$$. So vertex is at $(2, -1)$ with a minimum value of -1 since $$a>0$$. 7. Step 5: Summarize key points: - The parabola opens upwards. - x-intercepts at (1,0) and (3,0). - y-intercept at (0,3). - Vertex (minimum point) at (2,-1). This question introduces intercepts, factoring, vertex formula, and parabola shape.