This exercise set contains various questions focused on functions, including parabolas, linear equations, and solving quadratic equations. Let's break down each part:

1. Graph Analysis (f and p)

You are asked to read coordinates from the graphs of $f$ and $p$ and solve the following:

• a) Find the value of $f(-2.5)$.
  • From the graph of function $f$, locate $x = -2.5$ and find the corresponding $y$-value.
• b) Given $f(0.5) =$ and $f( \_ ) = 1.5$, find the missing values by looking at the graph of function $f$.
• c) Find the points where $p(1) = \_$ and $p(2) = \_$ using the parabola $p$.
• d) Solve $p(x) = 0$, which means finding the $x$-intercepts of parabola $p$.

2. Parabola $p$ Equation

• Identify the vertex of the parabola $p$ and form its equation in vertex form: $p(x) = a(x - h)^2 + k$.
• Find the precise value of $p(2.5)$ from the graph.

3. Line $g$

• Determine the slope $m$ and y-intercept $b$ of the line $g$.

4. Comparing Functions

• Compare the functions $h(x) = 2x - 3$, $y = 2x - 3$, and $a(x) = 8x - 8$, particularly when $x = 8$.

5. Solving the Quadratic Equation

• Solve $x^2 - 2x = 3$ and explain what the solutions represent in the context of the graph.

6. Equation $g(x) = p(x)$

• Solve $g(x) = p(x)$, noting that the solutions are $x = 0$ and $x = 3$. Discuss the significance of these solutions graphically.

7. Parallel Line to $g$

• Find the equation of a line parallel to $g$ with slope $1$ and a negative y-intercept, ensuring it intersects the parabola at $x = 1.5$.

8. Solutions of $f(x) = p(x)$

• Analyze the intersection points of $f(x) = p(x)$, particularly $x = -1$, and find the linear equation corresponding to $f(x)$.

9. Parabola through $D, F,$ and $I$

• Form the equation of the parabola that passes through these points and explain why this is unique.

10. Two Parabolas through $D$ and $F$

• Discuss how multiple parabolas can pass through the points $D$ and $F$.

Would you like detailed solutions for specific questions or further clarification? Here are five related questions to expand your understanding:

1. How do you derive the vertex form of a parabola from its graph?
2. What is the significance of the x-intercepts in solving quadratic equations graphically?
3. How can you calculate the slope of a line from a graph?
4. What happens to the solution when comparing different linear functions at specific x-values?
5. How does shifting a line parallel to itself affect its equation?

Tip: For solving quadratic equations graphically, always check where the graph intersects the x-axis for real solutions.