## Finding Points of Intersection for Complex Equations

#### Aligned To Common Core Standard:

**High School** - HSA-REI.D.11

How to Find Points of Intersection for Complex Equations?
Let's learn how to find points of intersection for complex equations. Suppose that you have a quadratic equation. In a linear-quadratic system where it is showing a parabola, and a straight line and the solution needs to be found for the points where the line is intersecting the parabola. The next step involves comparison where the values are compared to y resulting in both the equation in x.
The factors that are obtained are showed by finding the x coordinates. Now the value of x is substituted within the original equation for obtaining the value of y. Finally, through this the value of point of intersections is obtained. For example:
Y = 3x^{2} - 2x + 5 (parabola equation), y = 2x + 9 (straight line equation)
3x^{2} - 2x + 5 = 2x + 9 | 3x^{2} - 2x + 5 - 2x - 9 = 0 | 3x^{2} - 2x - 2x + 5 - 9 + 0 | 3x^{2} - 4x - 4 = 0.
The factors of these trinomials are: (3x + 2) (x - 2) = 0.
We now find the two sets of value coordinates by putting each value of x that comes from: 3x + 2 = 0 and x - 2 = 0 The two coordinates that are achieved will be the points of intersection for the straight line on the parabola. These worksheets will help students learn to make sense of complex equations to find where they hit intercepts and other equations on a graph.

### Printable Worksheets And Lessons

- Where is the Point?
Step-by-step Lesson- Where do the two parabolas meet up?

- Guided Lesson
- After you answer one, the other two are pretty easy. Take your
time.

- Guided Lesson Explanation
-Each questions gets it's own page for this explanation.

- Practice Worksheet
- Time to find that point. They bump into each other where?

- Matching Worksheet
- Match the complex equations and their point of intersection.

#### Homework Sheets

The best way I find to approach these is to get the equations in the same format and then proceed.

- Homework 1 - Find the points of intersection for the equations.
- Homework 2 - We have to solve the equations and work off of their values.
- Homework 3 - Now we got x value to check: x = -13. We put the x value in the equations.

#### Practice Worksheets

On some of these, you will look at the equations and swear that they couldn't possibly cross each other.

- Practice 1 - Find any one point of intersection for the following equations.
- Practice 2 - f(x) and g(x) will get it done.
- Practice 3 - Where do they meet?

#### Math Skill Quizzes

For the quizzes remember that you just find the answer, not the explanation.