Graphing Quadratics

Question

y=2x^2-20x+42 x values 1 to 8 

b) what is the vertex
c) what is the x-intercept
d) what is the y-intercept
e) factor the expression
f) what is the equation in vertex form

Answer 1

y = 2x² - 20x + 42  D: [1, 8]

 

b)  x_v = -b/2a = 20/4 = 5

     f(5) = 50 - 100 + 42 = -8

     V: (5, -8)

 

c) x intercepts happen where y = 0

    0 = 2x² - 20x + 42      set equal to 0

    0 = x² - 10x + 21        divide everything by common factor 2

    0 = (x-3)(x-7)             factor

    x = 3, 7                      apply zero product rule

    x intercepts:  (3, 0) and (7, 0)

 

d) y intercept happens where x = 0

    but the domain does not include x = 0, so there is no y intercept

 

e) y = 2(x-3)(x-7)

 

f) vertex form is obtained by completing the square:

 

y = 2(y² - 10x + 25) + 42 - 50

y = 2(y - 5)² -8