FST 'Quadratic Quiz'

250 days ago by mpaul

For each of the following find

  1. axis of symmetry
  2. vertex
  3. y-intercept
  4. x-intercepts

and sketch a cute little graph.

The graph does not need to be to scale.  Just cute.

1)  f(x) = x^2 - 9

2)  f(x) = x^2 - 8x + 15

3)  f(x) = 8x^2 - 2x - 15

4)  f(x) = x^2 - x - 1

5)  f(x) = ax^2 + bx + c
a,b,c = var('a b c') f(x) = a*x^2 + b*x + c show(f) 
       

a)  The line x = h is the axis of symmetry.
h = -b/(2*a) show(h) 
       

b)  The point (h,k) is the vertex where k = f(h).
k = f(h) show((h,k)) 
       

c)  The y-intercept is f(0).
show(f(0)) 
       

d)  The x-intercepts are the roots of f, or the x values for which f(x) = 0.
discriminant = b^2 - 4*a*c distance = sqrt(discriminant)/(2*a) show([h-distance, h+distance]) 
       
show(plot(f,-2,2)+ line([(h,y) for y in [k-1..k+2]], linestyle='--',color='black')+ points([(h,k),(h-distance,0),(h+distance,0)],color='red')) 
       
factor(a*x^2+b*x+c)