I'll analyze the math problems from the image. Give me a moment to extract the equations and interpret their graphs.

Functions and Graph Analysis:

1. $f(x) = x^2 + x - 12$
   • Find the zeros by solving the quadratic equation:
     $x^2 + x - 12 = 0$ Factor: $(x - 3)(x + 4) = 0$ So, the zeros are $x = 3$ and $x = -4$.
   • These are the $x$-intercepts.

2. $f(x) = 5x^2 - 10x$
   Factor out the common term: $5x(x - 2) = 0$ So, the zeros are $x = 0$ and $x = 2$.
   • These are the $x$-intercepts.

3. $f(x) = 2x^2 - 10x - 12$
   Solve the quadratic by factoring or using the quadratic formula: $2x^2 - 10x - 12 = 0$
   Divide by 2: $x^2 - 5x - 6 = 0$ Factor: $(x - 6)(x + 1) = 0$ So, the zeros are $x = 6$ and $x = -1$.
   • These are the $x$-intercepts.

4. $f(x) = 3x^2 - 21x + 18$
   Factor: $3(x^2 - 7x + 6) = 0$ Factor further: $3(x - 6)(x - 1) = 0$ So, the zeros are $x = 1$ and $x = 6$.
   • These are the $x$-intercepts.

Do you want detailed explanations on how I solved these?

Related Questions:

1. How do you derive the quadratic formula from completing the square?
2. What are tips for factoring complex quadratic equations?
3. How do graph features help predict the number of real zeros?
4. How does the discriminant affect the nature of the solutions for a quadratic equation?
5. How can graphing technology help verify solutions?

Tip: Always check your factors by expanding to ensure they match the original equation.