Question

graph each quadratic function and identify its key characteristics. f(x) = x^2 - 2x - 3

Answer 1

Answer:

See graph

Step-by-step explanation:

We want to graph the function $f(x)=x^2-2x-3$.

Let us rewrite this function in the vertex form so that we can graph it easily.

We achieve this by completing the square as follows;

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

$\Rightarrow f(x)=(x-1)^2-1-3$.

$\Rightarrow f(x)=(x-1)^2-4$.

Comparing to  $f(x)=a(x-h)^2+k$,  we have $a=1\:>\:0$,this means the graph will open up.

where $(h,k)=(1,4)$ is the vertex of the quadratic graph.

To find the y-intercept we put $x=0$ into the function to get,

$f(0)=(0-1)^2-4=-3$.

To find the x-intercept, we put $f(x)=0$.

$(x-1)^2-4=0$.

$(x-1)^2=4$.

$x-1=\pm \sqrt{4}$.

$x-1=\pm 2$.

$x=1\pm2$.

$x=-1,x=3$

With the nature of graph in mind, taking into consideration, the vertex and the intercepts, we draw the graph to obtain the quadratic graph in the attachment.