Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - Quadratics - Drawing parabolas.
Test Yourself 1.


 

Basic shapes 1.
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Drawing parabolas. For the following questions 3 to 8, draw the parabola and mark the coordinates of any intercepts and the vertex.
  3. Draw the parabola y = x(x - 3)
  4. Draw the parabola y = (x + 2)(x - 4)
  5.Draw the parabola y = -x(x + 2)
  6. Draw the parabola y = x2 - 2x - 3
  7. Draw the parabola y = 2x2 - 5x - 12
  8. Draw the parabola y = (x + 3)2
Transformations 9. By referencing the standard parabola y = x2, what movements must happen to develop the parabola y = (x - 2)2 + 4?
  10. By referencing the standard parabola y = x2, what movements must happen to develop the parabola y = 3(x + 3)2 -6?
  11. By referencing the standard parabola y = x2, what movements must happen to develop the parabola 2y = (x +1)2?
  12. By referencing the standard parabola y = x2, what movements must happen to develop the parabola y = (2x - 3)2 - 1?
Drawing parabolas by completing the square. For the following questions 13 to 18, complete the square for the given equation and then draw the parabola and mark the coordinates of any intercepts and the vertex.
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  16. y = 4x2 + 5x - 2
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Interpreting graphs.

19. Justin is wanting to maximise the area he can use in a rectangular garden plot in a nearby park. He develops the equation Area = x(40 - x) to link the length and breadth of the garden to help him plan.

As any good mathematician would do, Justin also draws a graph of his equation.

(i) Draw the graph which Justin did. The vertical axis is A. Mark in the intercepts.

(ii) Using the graph, find the value for x (the length) which will give the maximum area for the garden.

 
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