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10-3 Solving Quadratic Equations by Graphing — Practice Questions

  1. 1. Rewrite $x^2 + 7x = 12$ in standard form $ax^2 + bx + c = 0$. The value of $c$ is ___.

  2. 2. Which of the following is the standard form of $3x^2 = 4x - 1$?

    • A. $3x^2 - 4x + 1 = 0$
    • B. $3x^2 + 4x - 1 = 0$
    • C. $3x^2 - 4x - 1 = 0$
    • D. $3x^2 + 4x + 1 = 0$
  3. 3. What is the related quadratic function for the equation $5x - x^2 = 6$ once written in standard form?

    • A. $f(x) = x^2 - 5x + 6$
    • B. $f(x) = -x^2 + 5x - 6$
    • C. $f(x) = x^2 + 5x - 6$
    • D. $f(x) = x^2 - 5x - 6$
  4. 4. Rewrite $4x^2 - 3 = 9x$ in standard form. The value of $b$ is ___.

  5. 5. Which correctly identifies $a$, $b$, and $c$ after rewriting $6x - 2x^2 = 4$ in standard form?

    • A. $a = 2,\ b = -6,\ c = 4$
    • B. $a = -2,\ b = 6,\ c = -4$
    • C. $a = 2,\ b = 6,\ c = 4$
    • D. $a = -2,\ b = -6,\ c = 4$
  6. 6. When solving a quadratic equation by graphing its corresponding function, what feature of the parabola represents the solutions to the equation?

    • A. The vertex
    • B. The y-intercept
    • C. The x-intercepts
    • D. The axis of symmetry
  7. 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. 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?

    • A. $x = 5$ and $x = -2$
    • B. $x = -5$ and $x = 2$
    • C. $x = 10$ and $x = -1$
    • D. $x = -10$ and $x = 1$
  9. 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. 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?

    • A. $(0, -2)$ and $(0, 9)$
    • B. $(-2, 0)$ and $(9, 0)$
    • C. $(-2, 9)$
    • D. There is not enough information.