# How do you find the vertex and the intercepts for #-3x^2+12x-9#?

##### 1 Answer

vertex: maximum point(2,3)

Y-intercept = -9

X-intercept = 1 and 3

#### Explanation:

The given equation is

Given that the coefficient(constant number in front) of

Note for a POSITIVE coefficient, the graph is a HAPPY smiley (has a minimum point).

Complete the square to find the vertex:

In this form

the constant 3 is the y coordinate of the vertex.

And (x-2) = 0 is the x coordinate of the vertex, equate for x,

x=2 is the x coordinate. Hence the vertex is (2, 3).

To find the intercepts:

For y-intercept, equate x=0,

y= -9 is the y coordinate of the y-intercept.

For x-intercept, equate y=0, then factorise to find the 2 x intercepts,

Hence, the factors of the equation is (-3x+3) and (x-3), solve for x,

(x-3) =0,

x=3

Hence the x intercepts are x=1 and x =3.