Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function

B

given the equation of a parabola in standard form

y = ax² + bx + c : a ≠ 0

then the equation of the axis of symmetry which is also the x- coordinate of the vertex is obtained using

x = -

y = 4x² + 5x - 1 is in standard form

with a = 4, b = 5 and c = - 1

= -

hence axis of symmetry is x = -

to find the y-coordinate of the vertex substitute the x-coordinate into the equation

y = 4(- )² + 5(- ) - 1

  = - -

  = - = - 2

vertex = ( - , - 2 )

true

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: