What are the important points needed to graph #f(x)= x^2 - 10x + 5#?

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Answer 1 · 2018-08-12T07:11:22

Vertex #(5, -20)#
y-intercept #(0,5)#
x-intercepts #(sqrt20+5, 0); (-sqrt20-5,0)#

Given-

#f(x) =x^2-10x+5#

#y=x^2-10x+5#

The important points are - Vertex, y-intercept and x-intercepts

Vertex

#x=(-b)/(2a)=10/2=5#

At #x=5; y=5^2-10(5)+5=25-50+5=-20#

Vertex #(5, -20)#

Y-intercept

At #x=0; y=0^2-10(0)+5=5#

y-intercept #(0,5)#

x-intercepts

At #y=0;x^2-10x+5=0#

#x^2-10x=-5#

#x^2-10x+25=-5+25=20#

#(x-5)^2=20#

#x-5=+-sqrt20#

#x=sqrt20+5#

#x=-sqrt20-5#

x-intercepts #(sqrt20+5, 0); (-sqrt20-5,0)#

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