Quadratic functions

Question

Given the quadratic function f(x)=3x²+12x-63

a. Write the function in standard (vertex) form

b. Find the vertex of the function

c. Find the zeros of the function

 

Please show how you got the answers

Thanks!

Answer 1

f(x) = 3x² + 12x - 63

f(x) = 3(x² + 4x     ) - 63            factor out 3

f(x) = 3(x² + 4x + 4) - 63 - 12   complete the square

f(x) = 3(x + 2)² - 75

 

Vertex: (-2, -75)

 

0 = 3(x + 2)² - 75

75 = 3(x + 2)²

25 = (x + 2)²

±5 = x + 2

 

(-7, 0), (3, 0)