1. Rewrite $x^2 + 7x = 12$ in standard form $ax^2 + bx + c = 0$. The value of $c$ is ___.
2. Which of the following is the standard form of $3x^2 = 4x - 1$?
3. What is the related quadratic function for the equation $5x - x^2 = 6$ once written in standard form?
4. Rewrite $4x^2 - 3 = 9x$ in standard form. The value of $b$ is ___.
5. Which correctly identifies $a$, $b$, and $c$ after rewriting $6x - 2x^2 = 4$ in standard form?
6. When solving a quadratic equation by graphing its corresponding function, what feature of the parabola represents the solutions to the equation?
7. The graph of the function $y = x^2 - 9x + 14$ is a parabola that intersects the x-axis at $x=2$ and $x=7$. What is the smaller solution to the equation $x^2 - 9x + 14 = 0$? ___
8. To solve the equation $x^2 + 3x - 10 = 0$, you graph the function $y = x^2 + 3x - 10$. The parabola crosses the x-axis at $x = -5$ and $x = 2$. What are the solutions?
9. The graph of the function $y = x^2 - 64$ is a parabola. The solutions to the equation $x^2 - 64 = 0$ are the $x$-intercepts of this graph. What is the positive solution to the equation? ___
10. If the solutions to a quadratic equation are $x = -2$ and $x = 9$, what are the x-intercepts of the graph of the corresponding quadratic function?