Question

How would I graph -x+2=x^{2}

Answer 1

first you get the whole equation on one side

x^2 +x-2=0

after that you plug in x values to get y values.

plug 0 for x we get -2 for y. so our first point (0,-2)

plug 1 for x we get 0 for y so second point (1,-2)

you can continue graphing more points

Answer 2

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Usually, when we talk about graphing an equation, we want to graph something of the form ...

  y = f(x)

Here, you have an equation with no dependent variable, so the graph of it is a graph of the two points that satisfy the equation. The graph would be a number line with points at -2 and 1.

__

If you want to graph something of the form ...

  y = f(x)

you can define two functions: one for the left side of the equation, and one for the right side:

  f(x) = -x +2

  g(x) = x^2

These are graphed in the conventional way: find points on the curve and plot a curve through them. Graphs of these functions are shown as solid lines in the second attachment. The solutions to the equation are the x-values of the points where the graphs intersect each other.

__

For many purposes, it is convenient to rewrite the equation to one that is of the form ...

  f(x) = 0

Here, we can do that by subtracting the left-side expression to get the standard-form quadratic ...

  x^2 +x -2 = 0

In this form, the graph of f(x) = x^2 +x -2 is shown as the dashed green line in the attachment. The solutions are the values of x that make f(x) = 0. These are also called the x-intercepts—points where the graph intercepts the x-axis.

Factoring the above equation gives ...

  (x +2)(x -1) = 0

The values of x that make these factors be zero are the solutions to the equation: x = -2, x = 1.