How do you graph, label the vertex, axis of symmetry and x intercepts of y=(3x-1)(x-3)?

2 Answers
Jun 23, 2017

graph{(3x-1)(x-3) [-20, 20, -10, 10]}
Vertex = ( 5/3, -8/3)
Axis of symmetry = x=5/3
X-intercepts = (1/3,0) and (3,0)

Explanation:

Multiplying the two brackets we get the quadratic,
3x^2-10x+3
Comparing with ax^2+bx+c, we get
a=3 , b=-10, c=3
and the Discriminant = b^2-4ac => 64
Co-ordinates of Vertex of parabola are (-b/(2a),-D/(4a))
plug the the values of a,b,c to get vertex of parabola.

Axis of symmetry is the x-coordinate of Vertex i.e
x=5/3

x-intercept of the parabola is basically the roots of equation.
Roots can be obtained by equating the function to 0.
=>(3x-1)(x-3)=0
either 3x-1=0 or x-3=0 (By Zero Product Rule)
this gives x=1/3 , 3
These are the x-intercepts.

Jun 23, 2017

X-intercept

x=1/3
x=3
Vertex (5/3, -16/3)
Axis of symmetry x=5/3

Explanation:

Given -

y=(3x-1)(x-3)

X-intercept
At y=0

(3x-1)(x-3)=0

3x=1
x=1/3

x=3

y=3x^2-x-9x+3
y=3x^2-10x+3

Vertex

x=(-b)/(2a)=(-(-10))/(2 xx3)=10/6=5/3

At x=5/3

y=3(5/3)^2-10(5/3)+3
y=3(25/9)-50/3+3
y=25/3-50/3+3
y=(25-50+9)/3=-16/3

Vertex (5/3, -16/3)

Axis of symmetry x=5/3

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