How do you use the important points to sketch the graph of #f(x) = x^2 - 3x + 5#?

1 Answer
Aug 9, 2018

Refer Explanation section

Explanation:

Given -

#f(x)=x^2-3x+5#

We shall have it as -

#y=x^2-3x+5#

Important points are -
Vertex
y - intercept
x-intercepts

VERTEX

#x=(-b)/(2a)=(-(-3))/(2 xx 1)=3/2#

At #x=3/2; y=(3/2)^2-3(3/2)+5=9/4-9/2+5=(9-18+20)/4=(-4)/4=11/4#
Vertex #(3/2, 11/4)#

Y-INTERCEPT

At #x=0; y=(0^2)-3(0)+5=5#

x-intercept #(0,5)#

X-INTERCEPT

The minimum point of the curve is #(3/2, 11/4)#.

The y-intercept #(0,5)# is above the minimum point.

The curve is facing up.

Hence the curve has no x-intercepts.

With these two pieces of information, we can fix the curve.

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