Question

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

Answer 1

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.