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