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9th grade Graph y = ax² + bx + c, and match equations, tables and graphs worksheet

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Graph y = ax^2 + bx + c, and match equations, tables and graphs

Grade 9 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Esme graphs a skate ramp with y = x² - 6x + 5. What is the vertex? Type its x-value, then its y-value, with a comma between.

  2. Jun graphs a cereal bowl with y = 2x² - 12x + 11. What is the vertex? Type its x-value, then its y-value, with a comma between.

  3. Luz graphs a basketball shot with y = -2x² + 16x - 25 (nothing but net, on paper). What is the vertex? Type its x-value, then its y-value, with a comma between.

  4. Milo draws a lake bottom on a map with y = x² + 10x + 22. What is the vertex? Type its x-value, then its y-value, with a comma between.

  5. Noah has four graph cards and the equation y = -x² + 2x + 3. Which graph matches the equation?

    • Opens down, vertex (1, 4), crosses the y-axis at 3
    • Opens down, vertex (0, 3), crosses the y-axis at 3
    • Opens up, vertex (1, 4), crosses the y-axis at 3
    • Opens down, vertex (-1, 0), crosses the y-axis at 3

  6. Pia sorts graph cards for y = x² + 4x - 5. Which graph matches the equation?

    • Opens up, vertex (0, -5), crosses the y-axis at -5
    • Opens up, vertex (2, 7), crosses the y-axis at -5
    • Opens up, vertex (-2, -9), crosses the y-axis at -5
    • Opens down, vertex (-2, -9), crosses the y-axis at -5

  7. Ren sorts graph cards for y = 2x² + 8x - 3 (one card has a juice stain). Which graph matches the equation?

    • Opens up, vertex (-2, -11), crosses the y-axis at -3
    • Opens up, vertex (2, 21), crosses the y-axis at -3
    • Opens up, vertex (0, -3), crosses the y-axis at -3
    • Opens down, vertex (-2, -11), crosses the y-axis at -3

  8. Tala matches y = -x² - 6x - 5 to a graph of a ball's toss. Which graph matches the equation?

    • Opens down, vertex (3, -32), crosses the y-axis at -5
    • Opens up, vertex (-3, 4), crosses the y-axis at -5
    • Opens down, vertex (-3, 4), crosses the y-axis at -5
    • Opens down, vertex (0, -5), crosses the y-axis at -5

  9. Zee's table for a fountain sketch, y = x² + 2x - 5, has the row 3 | 10. Another input gives the same output. What is that input?

  10. Ari's table for a ramp, y = x² - 6x + 2, has the row -1 | 9. Another input gives the same output. What is that input?

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9th grade Graph y = ax² + bx + c, and match equations, tables and graphs worksheet – printable
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About this worksheet

Graph quadratics in standard form, and match equations, tables and graphs. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can fill in a table for y = ax² + bx + c, including negative inputs.
  • I can find the mirror (axis of symmetry) and the vertex from the equation.
  • I can match an equation to its table or graph by the opening, the mirror and the y-intercept.

Standard: F-IF.C.7a, F-IF.B.4

Words to know

parabola: The U-shaped graph of y = ax² + bx + c.

vertex: The turning point: the lowest or highest point.

axis of symmetry: The mirror line x = -b/(2a) through the vertex.

mirror rows: Two table rows the same distance from the mirror, with equal outputs.

opens up / down: a above 0 opens up; a below 0 opens down.

Common mistakes

Your child treated a negative number squared as negative, so (-2)² became -4.

Your child got the sign wrong when multiplying the middle number by a negative input.

Your child multiplied by the front number before squaring.

What to say

Ask: what is (-2) × (-2)?

Ask: is -4 × -2 positive or negative?

Ask: in 2x², what is squared, x or 2x?

Questions parents ask

What is the most common mistake with graph y = ax² + bx + c, and match equations, tables and graphs?

Your child treated a negative number squared as negative, so (-2)² became -4.

How can I help my child with graph y = ax² + bx + c, and match equations, tables and graphs?

Ask: what is (-2) × (-2)?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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