Quadratic and linear Intersection

In summary: Please clarify.In summary, the question asks how many points of intersection the line y = x has with the parabola y = 6x − x2 −10. The possible answers are A) none, B) one, C) two, D) three, or E) more than three. The student's attempt at a solution involved setting the equations equal to each other and using the quadratic formula to find the number of intersections. The student initially forgot to include the = sign in their attempted solution, but later realized that the correct answer is A, which is none.
  • #1
master_333
25
0

Homework Statement


How many points of intersection does the line y = x have with the parabola y = 6x − x2 −10 ?
A) none
B) one
C) two
D) three
E) more than three

Homework Equations

The Attempt at a Solution


x = 6x - x^2 - 10
-x^2+5x - 10
Used b^2 - 4ac to check the number of intersections.

The answer I got is . However my teacher marked it as incorrect. I still cannot find the problem, please help. If my teacher marked it wrong, please tell me so because I think he did. Thanks.
 
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  • #3
master_333 said:

The Attempt at a Solution


x = 6x - x^2 - 10
-x^2+5x - 10
Used b^2 - 4ac to check the number of intersections.

The answer I got is . However my teacher marked it as incorrect. I still cannot find the problem, please help. If my teacher marked it wrong, please tell me so because I think he did. Thanks.

What was your answer? What did you plug in for b2 - 4ac? Your approach is correct, but I'd draw a graph to be sure. (Hint: you know the parabola is negative, and you know the y-intercept is -10.)
 
  • #4
master_333 said:

Homework Statement


How many points of intersection does the line y = x have with the parabola y = 6x − x2 −10 ?
A) none
B) one
C) two
D) three
E) more than three

Homework Equations

The Attempt at a Solution


x = 6x - x^2 - 10
-x^2+5x - 10
Where did the = go? You have it two lines above, but not in the line above here.
master_333 said:
Used b^2 - 4ac to check the number of intersections.

The answer I got is .
Is what?
master_333 said:
However my teacher marked it as incorrect.
Your teacher marked what as incorrect?
You need to give us enough information so that we can provide meaningful help.
master_333 said:
I still cannot find the problem, please help. If my teacher marked it wrong, please tell me so because I think he did. Thanks.
 
  • #5
Sorry I know the right answer now. However I typed it in wrong. I forgot to write that the answer i got is A . Thanks
 
  • #6
master_333 said:
Sorry I know the right answer now. However I typed it in wrong. I forgot to write that the answer i got is A . Thanks
Are you saying that your teacher's answer is not A, or that you typed the question wrongly (or both)?
 

FAQ: Quadratic and linear Intersection

1. What is the difference between a quadratic and linear equation?

A quadratic equation is a polynomial equation with the highest degree of 2, meaning it contains an x2 term. A linear equation, on the other hand, is a polynomial equation with the highest degree of 1, meaning it does not contain an x2 term.

2. How do you solve for the intersection of a quadratic and linear equation?

To find the intersection point, you can set the two equations equal to each other and solve for the value of x. This will give you the x-coordinate of the intersection point. To find the y-coordinate, plug the x-coordinate into either of the equations and solve for y.

3. Can a quadratic and linear equation have more than one intersection point?

Yes, a quadratic and linear equation can have more than one intersection point. This can happen when the two equations have different slopes and intersect at multiple points.

4. What are the applications of quadratic and linear intersection in real life?

Quadratic and linear intersection can be used to solve problems involving projectile motion, such as finding the maximum height or distance of a thrown object. It is also used in economics and business to find the break-even point or optimal price for a product.

5. Is there a specific method to graph the intersection of a quadratic and linear equation?

To graph the intersection of a quadratic and linear equation, you can plot the two equations on the same coordinate plane and find the point(s) where they intersect. You can also use the quadratic formula to find the x-intercepts of the quadratic equation and then plot those points on the graph.

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