Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. T

Globokim8 2021-06-15 Answered

Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another way to find the intersection without using a graph.

a. Name the algebraic methods you already know to solve linear systems.

b. Use one of the methods you listed in part

(a) to solve for the intersection of \(\displaystyle{y}={x}^{{2}}−{3}{x}−{10}\) and \(y=−2x+2\). Carefully record your steps. Be sure to collaborate with your teammates and check your results along the way. Keep your work for this problem in a safe place. You will need it later in this lesson.

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Latisha Oneil
Answered 2021-06-16 Author has 14098 answers

a. At this point, we know three methods: Equal Values Mwthod, Substitution Method, and Elimination Method.
b. Since both equations have y isolated, we can use the Equal Values Method then solve for x: \(\displaystyle{x}^{{2}}-{3}{x}-{10}=-{2}{x}+{2}\)
Write in standart form: \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\)
\(\displaystyle{x}^{{2}}-{3}-{12}={0}\)
Factor the left side: \((x+3)(x-4)=0\)
By Zero Product Property, \(x+3=0\)
\(x=-3\)
\(x-4=0\)
\(x=4\)
Solve for the corresponding y-values. I used the first equation. When x=-3,
\(y=-2(-3)+2\)
\(y=6+2\)
\(y=8\)
When \(x=4\), \(y=-2(4)+2\)
\(y=-8+2\)
\(y=-6\)
So, the points of intersection are: (-3.8) and (4,-6)

Have a similar question?
Ask An Expert
30
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-24
Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another way to find the intersection without using a graph. a. Name the algebraic methods you already know to solve linear systems. b. Use one of the methods you listed in part (a) to solve for the intersection of \(\displaystyle{y}={x}^{{2}}−{3}{x}−{10}\) and y=−2x+2. Carefully record your steps. Be sure to collaborate with your teammates and check your results along the way. Keep your work for this problem in a safe place. You will need it later in this lesson.
asked 2021-06-29

Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another way to find the intersection without using a graph. a. Name the algebraic methods you already know to solve linear systems. b. Use one of the methods you listed in part (a) to solve for the intersection of \(\displaystyle{y}={x}^{{2}}−{3}{x}−{10}\) and \(y=−2x+2\). Carefully record your steps. Be sure to collaborate with your teammates and check your results along the way. Keep your work for this problem in a safe place. You will need it later in this lesson.

asked 2021-05-30
At what point do the curves \(r_1(t)=t,4-t,35+t^2\) and \(r_2(s)=7-s,s-3,s^2\) intersect? (x,y,z)= Find angle of intersection, \(\theta\), correct to the nearest degree.
asked 2021-09-09

Find the point(s) of intersection of the following two parametric curves, by first eliminating the parameter, then solving the system of equations.
\(\displaystyle{x}={t}+{5},{y}={t}^{{{2}}}{\quad\text{and}\quad}{x}={\frac{{{1}}}{{{16}}}}{t},{y}={t}\)
a. (25, 400)
b. (1, 16)
c. (400, 16)
d. A and B
e. A and C

asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2021-05-20
Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let \(\displaystyle{F}_{{R}}\) be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question
...