A student draws two parabolas both parabolas cross the x axis at (-4,0) and (6,0) the y intercept of the first parabolas is (0,-12). The y intercept of the second parabola is (0,-24) what is the positive difference between the a values for the two functions that describe the parabolas

Answer:The positive difference between the a values is 0.5Step-by-step explanation:we know thatBoth parabolas cross the x axis at (-4,0) and (6,0)soThe general equation is[tex]y=a(x+4)(x-6)[/tex]Find the value of a in the first parabolaThe y-intercept is (0,-12)soFor [tex]x=0, y=-12[/tex]substitute[tex]y=a(x+4)(x-6)[/tex][tex]-12=a(0+4)(0-6)[/tex][tex]-12=a(-24)[/tex][tex]a=0.5[/tex]Find the value of a in the second parabolaThe y-intercept is (0,-24)soFor [tex]x=0, y=-24[/tex]substitute[tex]y=a(x+4)(x-6)[/tex][tex]-24=a(0+4)(0-6)[/tex][tex]-24=a(-24)[/tex][tex]a=1[/tex]Find the positive difference between the a values for the two functionsso[tex]1-0.5=0.5[/tex]