+4609 The parabola with equation \(y=ax^2+bx+c\) is graphed below:
The zeros of the quadratic \(ax^2 + bx + c\) are at x=m and x=n , where m>n . What is m-n ?
+128407 We know that
y = a(x - 2)^2 - 4
And the point (4,12) is on the graph....so...
12 = a(4 - 2)^2 - 4
12 = 4a - 4
16 = 4a
4 = a
So we have that
y = 4(x - 2)^2 - 4
y = 4(x^2 - 4x + 4) - 4
y = 4x^2 - 16x + 16 - 4
y = 4x^2 - 16x + 12
And to find the roots
0 = 4x^2 - 16x + 12 divide through by 4
0 = x^2 - 4x + 3 factor
0 = (x - 3) ( x - 1) set each factor to 0 and m = 3 and n = 1
So....m - n = 3 - 1 = 2
Here's a graph : https://www.desmos.com/calculator/yvxfjhlbkv
