Question

Graph f(x) = x2 + 2x - 3, label the function’s x-intercepts, y-intercept and vertex with their coordinates. Also draw in and label the axis of symmetry

Answer 1

Answer with explanation:

The given function : $f(x)=x^2+2x-3$

Using completing the squares, we have

$f(x)=x^2+2x+1-1-3$        [∵ $(x+1)^2=x^2+2x+1$]

$f(x)=(x+1)^2-4$      (1)

Comparing (1) to the standard vertex form $f(x)=(x-h)^2+k$ , the vertex of function is at (h,k)=(-1,-4)

For x-intercept, put f(x)=0 in (1), we get

$0=(x+1)^2-4\\\\\Rightarrow\ (x+1)^2=4$    

Square root on both sides, we get

$x+1=\pm2\\\\x+1=-2\ or\ \ x+1=2\\\\=x=-3\ \ or\ x=1$

∴ x intercepts : x= (-3,0) and (1,0)

For y-intercept put x=0 in (1), we get

$f(1)=(1)^2-4=1-4=-3$  

∴ y intercept : (0,-3)

Axis of symmetry : $\dfrac{-b}{2a}$

In $f(x)=x^2+2x-3$ , a=1 and b=2

Axis of symmetry=$\dfrac{-2}{2(1)}=-1$