Question

Question 5.20. Find the vertex form of the following quadratic functions. Use it to find the maximum or minimum output as well as the zeros of each function, if the zeros exist. Simplify your answers as much as possible, but do not use a calculator. a. f(x) = 2x2 - 4x +1 b. g(x) = 2x2 - 4x + 5

Just question B.

Answer 1

b)

g(x) = 2x^2 - 4x + 5

standard vertex form is

y = a ( x - h )^2 + k

so we can write

g(x) = 2 ( x - 1 )^2 - 2 + 5

g(x) = 2 ( x - 1) ^2 + 3

vertex form of equation is

g(x) = 2 ( x- 1)^2 + 3

minimum output is 3

to find zeros set equation to 0 and solve for x

2 ( x- 1)^2 + 3 = 0

subtract 3 from both sides

2 ( x- 1)^2 = - 3

dividing both sides by 2

( x- 1)^2 = - 3/2

taking square root on both sides

x - 1 = +- sqrt ( -3/2 )

x - 1 = +- i sqrt (6)/ 2

adding 1 on both sides

x = 1 +- i sqrt (6)/ 2

zeros are

x = 1 + i sqrt (6)/2 , 1 - i sqrt (6)/2