Quadratic Graphs · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Quadratic graphs and tables

Mathematics · Algebra · ages 13-14
Name ______________________   Date ____________

  1. The graph of y = x² + 2 has no x-axis crossings.

    Circle one:   True   False

  2. What is the y-value where y = x² + 8 meets the y-axis?

    Answer: ______________

  3. What shape does the graph of y = x² make?

    • A horizontal straight line
    • An upward-opening parabola
    • A circle centred at zero

  4. Every quadratic graph opens upward.

    Circle one:   True   False

  5. A table for y = x² - 16 contains the pairs (-4, 0) and (4, 0). What is the x-value of the left x-axis crossing?

    • -4
    • 4
    • -16

  6. You have calculated several coordinate pairs for a quadratic on both sides of its turning point. How should you use them to draw its graph?

    • Plot pairs, then join with straight segments.
    • Plot only x-values, then draw a horizontal line.
    • Plot only y-values, then draw a vertical line.
    • Plot pairs, then join with a smooth curve.

  7. Which rule fits both coordinate pairs (-2, 7) and (1, 4)?

    • y = x² - 3
    • y = x² + 3
    • y = 2x + 3
    • y = -x² + 3

  8. For y = x² - 6, what is y when x = -4?

    Answer: ______________

  9. A graph changes from y = x² - 4 to y = x² + 1. How does every point move?

    • Up 5 units
    • Down 5 units
    • Right 5 units
    • Left 5 units

  10. Freddy calculates y = x² - 2 at x = -3 as -9 - 2 = -11. Which step needs changing?

    • He added 2 after squaring instead of subtracting 2.
    • He squared the whole expression (-3 - 2) instead of just -3.
    • He used -9 for (-3)² instead of 9 before subtracting 2.
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Quadratic graphs and tables W1-mt_GZuoYaDdWd-s1

  1. True · Every square is nonnegative, so y is at least 2. It can never equal zero.
  2. 8 · At the y-axis, x = 0. Substitution gives y = 0² + 8 = 8.
  3. An upward-opening parabola · The graph of y = x² is an upward-opening parabola, with its lowest point at (0, 0).
  4. False · A negative x² coefficient gives a downward-opening parabola. For example, y = -x² opens downward.
  5. -4 · Both pairs have y = 0. The negative x-value, -4, is the left crossing.
  6. Plot pairs, then join with a smooth curve. · Plot complete coordinate pairs on scaled axes and join them with a smooth curve.
  7. y = x² + 3 · For y = x² + 3, x = -2 gives 7 and x = 1 gives 4. Each other rule fails at least one point.
  8. 10 · (-4)² = 16, then 16 - 6 = 10.
  9. Up 5 units · The constant increases from -4 to 1, a change of +5. Every y-value increases by 5 while x stays unchanged.
  10. He used -9 for (-3)² instead of 9 before subtracting 2. · (-3)² is (-3) × (-3) = 9, not -9. The correct y-value is 9 - 2 = 7.
Worksheet · LightMySky