Home > Book, Graphing > Finding the equation of a parabola given the axes intercepts

Finding the equation of a parabola given the axes intercepts

If we know where a parabola cuts the ‘x’ axes then we can ascertain its two factors.  The value of the ‘y’ intercept will enable us to do the relevant scaling required to get our equation.

Consider a curve that cuts the ‘x’ axis at -4 and 3 and the   ‘y’ axis at 6.



1 The factors must be (x + 4) and (x -3)
2 Let y = a(x + 4)(x – 3)
3 a×(4)×(-3) = 6
4 So a = -1/2
5 So y = -1/2(x + 4)(x – 3)

Now let’s see another example

The curve cuts the the axes at (2, 0), (4, 0) and (0,16).

1 The factors must be (x – 2) and (x -4)
2 Let y = a(x – 2)(x – 4)
3 a×(-2)×(-4) = 16
4 So a = 2
5 So y = 2(x – 2)(x – 4)

Questions to try

  1. Curve cuts the axes at (-4, 0), (2, 0) and (0,-8)
  2. Curve cuts the axes at (-2, 0), (4,0) and (0, 8 )
  3. Curve cuts the axes at (1, 0), (4, 0) and (0, 8 )
  4. Curve cuts the axes at (-4,0), (-1, 0) and (0, -8)
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Categories: Book, Graphing
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