Question

Graph the functions on the same coordinate plane.

Answer 1

Answer:

The correct options are,

-3, 1

Step-by-step explanation:

Given functions,

$f(x)=-2x$

$g(x)=x^2-3$

$f(x)=g(x)$

$\implies -2x=x^2-3$

$\implies x^2+2x-3=0$

By middle term splitting,

$x^2+3x-x-3=0$

$x(x+3)-1(x+3)=0$

$(x-1)(x+3)=0$

By zero product property,

x = 1 or x = -3

Hence, the required solutions are,

x = 1 and x = -3

Answer 2

A graph shows the solutions to be
.. x = -3
.. x = 1

Here's an analytic solution.
.. f(x) = g(x)
.. -2x = x^2 -3 . . . . . . substitute the given function definitions
.. 0 = x^2 +2x -3 . . . . add 2x
.. 0 = (x -1)(x +3) . . . . . factor

Use the zero-product rule to find values of x that are solutions. One or the other of the factors must be zero for the product to be zero.
.. x -1 = 0 . . . . first factor is zero
.. x = 1

.. x +3 = 0 . . . second factor is zero
.. x = -3