Graphing Intersection Points for y=3x^2 and y=3^x | Algebra Homework Help

In summary, the problem is to find the intersection points of the two equations y=3x^2 and y=3^x, which cannot be solved algebraically. The solutions are (-.451,.0609), (1.3), and (3, 27). Graphing techniques must be used to find these points, and a table of values or a graph can be used to estimate the solutions.
  • #1
ilii
39
1

Homework Statement



Find the intersection points of y=3x^2 and y=3^x

Homework Equations



They must be found with graphing techniques and cannot be proved algebraically. The answers are (-.451,.0609), (1.3), and (3, 27).

The Attempt at a Solution



Table of values from -3 to 3 for x, and i can come up with (1,3) and (3, 27). I really don't know how to find an intersection like (-.451,.0609).not sure which graph to post here...

for (3x^2)-(3^x)

http://www.meta-calculator.com/online/0gzp2kai8ehffor y=3x^2 and y=3^x separately

for (3x^2)-(3^x)

http://www.meta-calculator.com/online/0gzp2kai8ehf for y=3x^2 and y=3^x separately

http://www.meta-calculator.com/online/eqo7hgmc6lsf
and
http://www.meta-calculator.com/online/eqo7hgmc6lsf
 
Last edited:
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  • #2
draw the graph of the lines and post your drawing, else we cannot help you.
 
  • #3
On your graph of the difference, you can take the zeros. Use those for x and plug back into one of your equations to find y. Otherwise, plot the two functions on the same graph and do your best to estimate.
 
  • #4
ok thank you
 

FAQ: Graphing Intersection Points for y=3x^2 and y=3^x | Algebra Homework Help

What are points of intersection?

Points of intersection refer to the points where two or more lines or curves intersect on a graph. These points have the same coordinates on each line or curve, indicating that they share the same value for the variables.

How do you find points of intersection?

To find points of intersection, you must have two or more equations that represent lines or curves. You can then solve the equations together using algebraic methods or graphically by plotting the equations on a graph and identifying the coordinates of the intersection points.

Why are points of intersection important?

Points of intersection are important because they can help us find solutions to equations and systems of equations. They also allow us to visualize the relationships between multiple variables and understand how they intersect and interact with each other.

What is the significance of multiple points of intersection?

Multiple points of intersection can indicate that there are multiple solutions to an equation or system of equations. They can also show the range of possible values for the variables and provide insight into the behavior of the lines or curves in the graph.

How are points of intersection used in real-life applications?

Points of intersection are used in various fields, including engineering, physics, and economics, to solve problems and make predictions. They can help determine optimal solutions, identify critical points, and analyze data to make informed decisions.

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