10 Use the discriminant to predict the number of horizontal

10. Use the discriminant to predict the number of horizontal intercepts for each function. Then use the quadratic formula to find all the zeros. Identify the coordinates of any horizontal or vertical intercepts. a·y=2x2 + 3x-5 b, f(x) =-16 + 8x-z? c. f(x) = x2 + 2x + 2 d. y = 2(x-1)2 + 1 ng f, f(t) = (t + 2)(t-4) + 9

Solution

d) y = 2 ( x- 1)^2 +1

y = 2 ( x^2 - 2x + 1 ) + 1

y = 2x^2 - 4x + 2 + 1

y = 2x^2 - 4x + 3

discriminant =( -8)

so, there are 2 imaginary solutions

applying quadratic formula

x = ( -b +- sqrt ( b^2 - 4ac ) / 2a

x = ( 4 + sqrt (-8) ) / 4 , x = ( 4 - sqrt (8)) / 4

y intercept = (0,3)

f) f(t) = ( t+2)(t-4) + 9

= t^2 + 2t - 4t - 8 + 9

= t^2 - 2t + 1

disciminant = 0

hence, equation will have 1 real solution

x = ( 2 +- sqrt ( 4 - 4) ) / 2

x = 1

x intecepts are (1,0)

and y intercept = (0,1)