Which system of equations can be graphed to find the solution(s) to x2 = 2x + 3?

Question

this may be the hardest section i have been in please help

Answer 1

Bob,

 

I assume this is x² = 2x + 3.  If so, then the function is a quadratic and can be written as:

 

x² - 2x - 3 = 0 (ax² + bx + c is the general form)

 

Now, factor the quadratic:

 

(x - 3)(x +1) = 0 (-3 and 1 because -3 + 1 = -2, the b coefficient and -3 * 1 = -3, the c coefficient)

 

Then, either, or both of the factors must equal 0 so:

 

x - 3 = 0 => x = 3 and

 

x + 1 = 0 => x = -1 

 

x must be -1 and 3 to solve this quadratic.

 

BTW, if you graph the quadratic, it will cross the x-axis at x = -1 and 3