How do you find the vertex and the intercepts for #-3x^2+12x-9#?
vertex: maximum point(2,3)
Y-intercept = -9
X-intercept = 1 and 3
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,
Hence the x intercepts are x=1 and x =3.