Write f(x)=1/2x^2+x-4 in intercept form.

Question

Write f(x)=1/2x^2+x-4 in intercept form.

Answer 1

This involves factoring the function.

Start by factoring out the leading coefficient of 1/2.

This will give you f(x)=1/2(x²+2x-8).

The trinomial inside the parentheses can be factored even further into f(x)=1/2(x+4)(x-2).

This is in intercept form because the graph will cross the x-axis when x+4=0 and x-2=0. Meaning, there are x-intercepts at x=-4 and x=2.

Answer 2

Solution:

This is the equation of a parabola y = f(x) = 1/2 x² + x - 4

The intercept form of the equation is y = a ( x-p)(x-q)

so first find the y intercept by setting x = 0, y = f(x) = 1/2( 0)² + 0 - 4 = -4

2nd find the the x intercepts by setting y = 0 , 0 = 1/2 x² + x - 4 , multiply both sides by 2

0 = x² + 2x - 8 , using factoring law ( x + 4) (x - 2) = 0, and the roots are x = -4 and x = 2 are also the x intercepts in point form ( -4, 0 ) , and ( 2 , 0) where p = -4 , and q = 2 , and x = p+q /2 = (-4+2)/2 = -1

substituting, -4 = a (-1 +4)(-1-2) = a (3)(-3) = a ( -9)

Find a, a = -4/-9 = 4/9 , and the equation in intercept form is y = 4/9 ( x +4 ) ( x -2)