Solving Equations Graphically

Solving Radical Equations Graphically

Follow along with your notes page

Warm-Up Problems

Complete warm-up problems #1-#4

Graph each equation without a calculator (I would state the transformations of the function first to help you graph!). Then state the domain and range. After you finish, check your work on the next few slides :)

Transformation:
None, it's the parent function
Domain:
[0, ∞) or x ≥ 0
Range:
[0, ∞) or y ≥ 0

Transformation:
Right 5
Domain:
[5, ∞) or x ≥ 5
Range:
[0, ∞) or y ≥ 0

Transformation:
Right 4
Domain:
[4, ∞) or x ≥ 4
Range:
[0, ∞) or y ≥ 0

Transformation:
Left 2 and Down 3
Domain:
[-2, ∞) or x ≥ -2
Range:
[-3, ∞) or y ≥ -3

​Solving Radical Equations Graphically - Is There a Solution?

We will do #1 and #4 "together" and you will do #6, #7, and #10 on your own. You will need graph paper. There should be some on my tall filing cabinet in the back, but please use your own or borrow from a friend if you are able to.

​Set up your graph paper like this:

Graph by hand on your graph paper:
*Graph the left side of the equation by hand
(Linear parent function, up 2, slope of -2). [RED]
* Graph the right side of the equation by hand on the same grid (Linear parent function, down 3, slope of 3). [BLUE]

​*Put a dot at the point of intersection - where the lines cross. This is at (1,0). This tells you the solution!

Conclusion:
*The solution, or answer, to the equation is x=1!
*The x-coordinate is the value for x that makes the left side of the problem equal the right side.
*The y-coordinate is the value of each side of the equation.

Solve algebraically (beside the graph on your paper):
-2x +2 = 3x - 3
-3x -3x subtract 3x from both sides
-5x + 2 = -3
-2 -2 subtract 2 from both sides
-5x = -5 divide both sides by -5
x = 1


Conclusion:
*The solution, or answer, to the equation is x=1!
*You should get the same solution solving both graphically and algebraically!

​Your paper should look like this

Graph by hand on your graph paper:
*Graph the left side of the equation
(Absolute value parent function, right 2). [GREEN]
*Graph the right side of the equation
(Constant parent function at y=3) [BLUE]
*Put a dot at the points of intersection - where the lines cross.
This is at (-1, 3) and (5,3). This tells you the solutions!

Conclusion:
*The solution, or answer, to the equation is x = -1 and x = 5! Two solutions this time!
*The x-coordinate is the value for x that makes the left side of the problem equal the right side.
*The y-coordinate is the value of each side of the equation.

​

Solve algebraically (beside the graph on your paper):
|x-2| = 3
We need 2 cases since this is an absolute value function
x - 2 = 3 x - 2 = -3
+2 +2 +2 +2
x = 5 x = -1
Reminder
|3| = 3 if we plug in our answer |5-2| = |3| = 3
|-3| = 3 if we plug in our answer |-1 -2| = |-3| = 3
Both solutions lead us to a final answer of 3 which is why we need the two cases!
Conclusion:
*The solution, or answer, to the equation is x = -1 and x = 5! Two solutions this time!
*You should get the same solution solving both graphically and algebraically!

​*If the lines do not intersect then you have no solution.

​Your paper should look like this:

Your turn!

Answer problems #6, #7, and #10! Keep your paper set up the same way.

Multiple Choice

What solution(s) did you get for #6?

• x = 2

• x = -2

• x = 0

• x = 2 or x = -2

• No solution

Multiple Choice

What solution(s) did you get for #7?

• x = -4

• x = -2

• x = 1

• No solution

Multiple Choice

What solution(s) did you get for #10?

• x = 0

• x = 1

• x = 0 or x = 1

• No solution

​This is what your paper should look like.

When you are finished

Plan for a CYU on Monday that will cover solving equations algebraically and graphically. The problems on the CYU will look like the ones we did in class together on Wednesday and the problems from this Quizizz lesson.

CYU on Monday

Put the printed notes page and your graph paper in the notes section of your binder

​Math Binder