Question

How do you write the quadratic function in intercept form given x intercepts 1,4 and point (3,2)?

Answer 1

`y=-(x-1)(x-4)`

Explanation:

`"given x-intercepts (roots) at " x=1" and "x=4`

`"then factors are " (x-1)" and " (x-4)`

`rArry=a(x-1)(x-4)`

`"to find a, substitute the point " (3,2)" into the equation"`

`rArr2=a(3-1)(3-4)=-2a`

`rArra=-1`

`rArry=-(x-1)(x-4)larrcolor(red)" in intercept form"`

Answer 2

`y= -x^2 +5x -4`

Explanation:

Since x intercepts are 1 and 4, x-1 and x-4 will be factors of the quadratic expression. Hence initially assume that the function is `y= (x-1)(x-4)` or `y= x^2 -5x+4`.

Next. point (3,2) has to satisfy the function. Now substitute x=3 in the equation and it is observed that it gives y=-2. To meet this requirement the initial assumption may be modified as `y= -x^2 +5x -4`, which meets all the given conditions.

This equation represents a vertical parabola opening down