Consider the quadratic function f(x)=−x^2+4x+12Determine the following:The smallest xx-intercept is x=Incorrect The largest xx-intercept is x= The yy-intercept is y=

Answer:The smallest x-intercept is x= -2The largest x-intercept is x=  6The y-intercept is y= 12Step-by-step explanation:We are given a function as follows:[tex]y=f(x)=-x^2+4x+12[/tex]The x-intercept of a function is the value of x where the function is equal to 0.i.e.[tex]y=f(x)=0[/tex][tex]-x^2+4x+12=0[/tex]i.e.[tex]x^2-4x-12=0\\\\x^2-6x+2x-12=0[/tex]( We used the method of splitting the middle term)[tex]x(x-6)+2(x-6)=0\\\\(x+2)(x-6)=0[/tex]i.e.[tex]x=-2\ and\ x=6[/tex]Hence, the smallest x-intercept is: x= -2and the largest x-intercept is: x=6The y-intercept is the value of y where x=0i.e. we have:[tex]y=-0^2+4\times 0+12\\\\y=12[/tex]