Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Which represents the solution(s) of the graphed system of equations, y = x2 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)

Sagot :

Answer: the second choice: (0, - 2) and (1, 0).

Explanation:

1) The solution of a graphed system of equations is the points of intersection of the equations.

2) Hence, this method requires to graph each function in one Cartesian coordinate system.

3) To graph the function y = x² + x  - 2, you can follow these steps

  • draw the perpendicular x(horizontal)-axis, and y(vertical)- axis
  • mark the divisions in each axis (1 unit is a good scale for this case)
  • notice that y = x² + x  - 2 is a parabola
  • write y = x² + x  - 2 in its vertex form following these steps:

      y = (x² + x)  - 2

      y + 1/4 =  (x² + x + 1/4)  - 2

       y + 1/4 = (x + 1/2)²  - 2

       y = (x + 1/2)²  - 2 - 1/4

       y = (x + 1/2)² - 9/4

       Compare with the vertex form y = (x + h)² + k, where the coordinates of the vertex are (h,k). Therefore, the vertex is (1/2, - 9/4).

  • The parabola open upwards (because the coefficient of the quadratic term is positive).
  • Find the y-intercept (x =0) and x-intercepts (y = 0), and write a table with some values:
  • x       y = (x + 1/2)² - 9/4
  • -2            0
  • -1           - 2
  • -1/2       -2.25
  • 0         - 2
  • 1/2         -1.25
  • 1             0
  • 2           4

4) To graph the function y = 2x - 2, you can follow these steps:

  • Use the same Cartesian coordinate system
  • Notice it is a line
  • The slope is 2 (the coefficient of x)
  • The y-intercept is - 2( the constant term)
  • Build a table (use the same x-values used for the first graph)
  • x        y = 2x - 2
  • -2          - 6
  • -1           - 4
  • -1/2       - 3
  • 0          - 2
  • 1/2        -  1
  • 1             0
  • 2            2

The tables show that these points are common to the two functions: (0, - 2) and (1,0).

The graphs are shown in the figure attached.

You can see that the parabola (blue curve) and the line (purple line) intercept each other at those two points ( 0, - 2) and (1,0).

View image Аноним
hinojoselijah

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.