# 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** **x intercepts are at** **and
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]