Question

Please help and show the steps.

How do you figure out the equation to graph it

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

Answer 1

Answer:

Graph of the given equation is a opening up parabola passing through origin (0,0) and (2,0) and having vertex (1,-1)

Step-by-step explanation:

parabola - it is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

vertex - The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.

the given equation can be resolved as:

$g(x)=(x-1)^2-1\\g(x) = x^2 -2x +1 -1\\g(x) = x^2 - 2x$

now substituting x = 0,

$g(x) = x^2 - 2x\\g(x) = (0)^2- 2(0)\\g(x) = 0$

therefore the equation satisfies the point (0,0)that is origin.

now putting g(x) = 0,

$g(x) = x^2 - 2x\\0 = x^2- 2x\\2x = x^2\\2=x$

so when y coordinate is 0 x coordinate is 2,

therefore the equation also satisfies the (2,0)

general equation of a parabola is

$f(x) = ax^2 + bx + c$

and the vertex of the parabola is given by  $\frac{-b}{2a}{,}{f{(}\frac{-b}{2a}{)}}$

given equation of parabola $g(x) = x^2 - 2x$

here a = 1 and b= -2

substituting in the vertex formula,

vertex of the parabola is ${(}{1}{,}{f{(}{1}{)}}{)}$

$f(1) = 1 - 2 = -1$

therefore the vertex is (1,-1).

so the parabola is passing through origin(0,0) and (2,0) with vertex (1,-1).

more about parabola at  brainly.com/question/21685473

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