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 2021-09-14 Answered
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
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Expert Answer

Yusuf Keller
Answered 2021-09-15 Author has 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)

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