Graphing function

Question

Graph the function f(x)= 3x² - 6x - 24. 
Label its y-intercept, x- intercepts, and vertex 

How do I do this? Please help 

Answer 1

Put the function into graphing form: f(x) = a(x - h)² + k

 

f(x) = 3x² - 6x                   - 24        Complete the square

f(x) = 3(x² - 2x + 1) - 24 - 3

f(x) = 3(x - 1)² - 27

 

Vertex = (1, -27)

 

x-intercepts are at f(x) = 0

 

0 = 3(x - 1)² - 27

27 = 3(x - 1)²

9 = 3(x - 1)²

3 = (x - 1)²

±√3 = x - 1

1 ±√3 = x

 

x-intercepts are at 1 ±√3.

 

y-intercepts are at x = 0.

 

y = 3(0 - 1)² - 27

y = - 3 - 27

y = - 30

 

The y-intercept is at -30.