What are the important points needed to graph f(x)=x2−10x+5?

1 Answer
Nallasivam V
Aug 12, 2018

Vertex (5,−20)
y-intercept (0,5)
x-intercepts (√20+5,0);(−√20−5,0)

Explanation:

Given-

f(x)=x2−10x+5

y=x2−10x+5

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

Vertex

x=−b2a=102=5

At x=5;y=52−10(5)+5=25−50+5=−20

Vertex (5,−20)

Y-intercept

At x=0;y=02−10(0)+5=5

y-intercept (0,5)

x-intercepts

At y=0;x2−10x+5=0

x2−10x=−5

x2−10x+25=−5+25=20

(x−5)2=20

x−5=±√20

x=√20+5

x=−√20−5

x-intercepts (√20+5,0);(−√20−5,0)

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