Question

Find the discriminant for the following guodutie function. Describe the number and Apes of roots it will have. Then find the roots. Write your answer in simplest radical form. Sketch a graph of the parabola using 5 points, including the vertex. f(x)= 1/2x^2-2x+10

Answer 1

• discriminant: -16, two complex conjugate roots
• roots: 2±4i
• graph: see attached

Explanation:

You want the discriminant, roots, and graph of the quadratic function ...

f(x) = 1/2x² -2x +10

Discriminant

The discriminant of the quadratic function

y = ax² +bx +c

is ...

d = b² -4ac

The given function has a=1/2, b=-2, c=10, so the discriminant is ...

d = (-2)² -4(1/2)(10) = 4 -20 = -16

The discriminant of -16 means there will be two distinct complex conjugate roots.

Roots

The roots are ...

x = (-b ±√d)/(2a)

x = (-(-2) ±√(-16))/(2(1/2)) = 2 ±4i

Graph

A graph of the function is attached.