Drawing parabola from given equation

Draw the graph of a quadratic equation by completing a two-column substitution table, matching each x-value with its y-value, and plotting the resulting parabola.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-9
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y10-09

Resources

Terminology

  • parabola
  • quadratic

Task goals

  • Plot an a=1 standard-form quadratic y=x^2+bx+c by completing a two-column Substitute x / y table.
  • Plot every ordered pair accurately and join the points with one smooth parabola.
  • Use equal y-values on either side of the turn to check substitution and plotting.
  • Label the turning point, axis of symmetry, and visible x-intercepts from the finished graph.
  • Choose a useful consecutive range of x-values that reveals both sides of the turning point.

Where this fits

What leads into this objective, and where it goes next.

Before

Comparing sequences: nth terms, graphs and intersection

Comparing sequences: nth terms, graphs and intersection

Gradient

Gradient

Forming equations of given straight line graph (using y=mx+c)

Forming equations of given straight line graph (using y=mx+c)

You are here

Drawing parabola from given equation

Drawing parabola from given equation

Do

Determining the effect on graphs in the coordinate plane of changing the coefficient of x^2 and the fixed value c, for a range of quadratic equations of the form y = ax^2 or y = x^2 + c, where a is a positive integer and c is an integer

Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y10-09

Next

Year 10 is the last year of this phase — the curriculum lists nothing after this. Extension resources: Drawing exponential graphs, Reading and forming parabolas in vertex form y = a(x - h)^2 + k where a is not 1.

Also under NA5-9:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.