A quadratic function f is given (a)Express f in standard form (b)Find the vertex and x- and y-intercepts of f. (c)Sketch the graph.(d)Find the domain and range of f.f(x)=x^{2}-2x+3

preprekomW

preprekomW

Answered question

2021-09-14

A quadratic function f is given
(a)Express f in standard form
(b)Find the vertex and x- and y-intercepts of f.
(c)Sketch the graph.
(d)Find the domain and range of f.
f(x)=x22x+3

Answer & Explanation

Yusuf Keller

Yusuf Keller

Skilled2021-09-15Added 90 answers

f(x)=x22x+3The standard form of quadratic equation is f(x)=a(xh)2+k
(1)(a)f(x)=x22x+1+2.f(x)=(x1)2+2
On comparing it with equation (1) we get:h=1,k=2(b) The vertex V is given by V=(h,k)=(1,2) The y−intercept is given by x=0

f(0)=3

So, we have (0,3) as the y−intercept.

Now the x−intercept is given by equating f(x)=0
x22x+3=0
x23x+x3=0x
(x3)+1(x3)=0
x=1,3So,xintercepts of fare(1,0)and(3,0)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?