How do you find the vertex and intercepts for #y=-3(x-3)(x+1)#?
2 Answers
Explanation:
#"to find the intercepts, that is where the graph crosses"#
#"the x and y axes"#
#• " let x = 0, in the equation for y-intercept"#
#• " let y = 0, in the equation for x-intercepts"#
#x=0toy=-3(-3)(1)=9larrcolor(red)" y-intercept"#
#y=0to-3(x-3)(x+1)=0#
#"equate each factor to zero and solve for x"#
#x-3=0rArrx=3#
#x+1=0rArrx=-1#
#rArrx=-1,x=3larrcolor(red)" x-intercepts"#
#color(blue)"the axis of symmetry"" is at the midpoint of the"#
#"x-intercepts"#
#rArrx=(-1+3)/2=1rArrx=1" is the axis of symmetry"#
#"the vertex lies on the axis of symmetry"#
#rArr" x-coordinate of vertex is "x=1#
#"substitute this value into the equation for y-coordinate"#
#rArry_(color(red)"vertex")=-3(-2)(2)=12#
#rArrcolor(magenta)"vertex "=(1,12)#
graph{-3(x-3)(x+1) [-40, 40, -20, 20]}
Vertex is at
y intercept is at
Explanation:
x intercepts can be found by putting
y intercept can be found by putting
y intercept is at
graph{-3(x-3)(x+1) [-40, 40, -20, 20]} [Ans]