Determine the roots and axis of symmetry for the following q

Determine the root(s) and axis of symmetry for the following quadratic functions. Enter your answer as a single number of a string of numbers. Separate multiple answers with commas and if there are no roots write DNE. (For example, if the roots are 3 and 4 enter 3,4).

Solution

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

y = x^2 +x -1

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

y = (x+1/2)^2 - 5/4

Vertex ( -1/2 , -5/4)

Parabola is upward facing , so the axis of symmetry : x = -1/2

Roots: x^2 +x -1 =0

x = (-1+/sqrt(1+4))/2

= -1.618 , 0.618

g(x) = (x+10(5x -1)

Roots : g(x) =0

x= -10 , x=1/5

Rewriting the equation : g(x) = 5x^2 +50x-x -10 = 5x^2 +49x -10

vertex of g(x) : x =-b/2a ; y = g(-b/2a)

x = -49/10 , y =-2601/20)

Upward facing parabola , Axis of symmetry : x = -49/10

h(x) = x^2 -x -42

Roots: h(x) =0

x^2 -x -42 =0

x = -6 ; x = 7

Vertex :   x =-b/2a ; y = h(-b/2a)

x = 1/2 , y = -169/4

upward facing parabola , axis of symmetry : x = 1/2