Question

A quadratic function f is given. f(x) = x² +4x +3 (b) Find the vertex and x- and y-intercepts of f. (If an answer does not exist, x-intercepts (x, y) = (______) (smaller x-value) (x, y) = (______) (larger x-value) y-intercepts (x, y) = (______)

Answer 1

Hi,

Explanation:

`y=f(x)=x^2+4x+3\\\\y=x^2+4x+4-1=(x+2)^2-1\\Vertex\ is\ (-2,-1)`

`y=x^2+4x+3=x^2+x+3x+3=x(x+1)+3(x+1)=(x+1)(x+3)\\`

Roots (x-intercepts) are x=-1 and x=-3

x-intercepts (x, y)=(-1,0) for smaller x-value

x-intercepts (x, y)=(-3,0) for larger x-value

`y=x^2+4x+3\\if\ x=0\ then\ y=3\\`

y-intercepts (x, y) =(0,3)