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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

Sagot :

Sqdancefanidn

Answer:

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

Step-by-step 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.

View image Sqdancefan
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