Lesson Worksheet: Solving Cubic Equations Graphically Mathematics

In this worksheet, we will practice graphing a cubic equation and using this graph to find its solution or solutions.

Q1:

Use technology to plot the graph of 𝑓(𝑥)=𝑥+5𝑥100, and use this graph to find the solutions to the equation 𝑥+5𝑥=100 to two decimal places.

  • A𝑥=3.44
  • B𝑥=3.44
  • C𝑥=12.81
  • D𝑥=7.03
  • E𝑥=7.03

Q2:

Use technology to plot the graph of 𝑓(𝑥)=𝑥+3𝑥2, and use this graph to find the solutions to the equation 𝑥+3𝑥=2 to two decimal places.

  • A𝑥=0.73, 𝑥=1, 𝑥=2.73
  • B𝑥=2.73, 𝑥=1, 𝑥=0.73
  • C𝑥=2.00, 𝑥=1.00, 𝑥=0.00
  • D𝑥=0.56, 𝑥=0, 𝑥=3.56
  • E𝑥=3.56, 𝑥=0, 𝑥=0.56

Q3:

The figure shows the graphs of the curve 𝑦=𝑥(𝑥1)(𝑥+2) and the line 𝑦=𝑘(𝑥1) for some 𝑘<0.

The graphs intersect at three points, one of which has 𝑥-coordinate 1. Find a quadratic equation whose roots are the 𝑥-coordinates of the other two points of intersection.

  • A𝑥(𝑥+2)+𝑘=0
  • B𝑥(𝑥+2)𝑘(𝑥1)=0
  • C𝑥(𝑥1)=𝑘
  • D𝑥(𝑥+2)𝑘=0
  • E𝑥(𝑥+2)=0

By considering the discriminant of this quadratic equation, find the slope of the line through (1,0) which is tangent to the curve at some other point.

At what point is this line tangent to the curve?

  • A(3,30)
  • B(0,0)
  • C(1,0)
  • D(1,2)
  • E(2,8)

Q4:

The graph of 𝑦=𝑥2𝑥 is shown in the figure. What line needs to be drawn to solve 1=𝑥3𝑥1?

  • A𝑦=𝑥+2
  • B𝑦=2
  • C𝑦=𝑥2
  • D𝑦=𝑥+1
  • E𝑦=𝑥1

Q5:

If the graph of the function 𝑓(𝑥)=𝑥6𝑥+11𝑥6 is as shown, use this graph to find the solution set to the equation 𝑥6𝑥+11𝑥=6.

  • A{1,3}
  • B{1,2}
  • C{1}
  • D{1,2,3}
  • E{2.3}

Q6:

The given figure shows the graph of 𝑓(𝑥)=𝑥4𝑥+1.

Use the graph to determine the number of solutions to the equation 𝑥=4𝑥1.

Use the graph to determine the intervals in which the solutions to 𝑥=4𝑥1 lie.

  • A0.5<𝑥<0, 0<𝑥<0.5, and 4<𝑥<5
  • B1<𝑥<0, 0<𝑥<1, and 3<𝑥<4
  • C0.5<𝑥<0, 0<𝑥<2, and 3<𝑥<4
  • D1<𝑥<0.5, 0.5<𝑥<0, and 3<𝑥<4
  • E1<𝑥<0, 0<𝑥<1, and 4<𝑥<5

Q7:

Use technology to plot the graph of 𝑓(𝑥)=𝑥𝑥𝑥+1, and use this graph to choose the best solution to the equation 𝑥+𝑥+𝑥=1.

  • A𝑥=1.039
  • B𝑥=0.544
  • C𝑥=0.544
  • D𝑥=1
  • E𝑥=1.039

Q8:

The graph of 𝑦=3𝑥+5𝑥3𝑥4 is shown in the figure. What is the equation of the line that needs to be drawn to solve 3𝑥+5𝑥5𝑥=7?

  • A𝑦=2𝑥3
  • B𝑦=3𝑥+2
  • C𝑦=2𝑥3
  • D𝑦=2𝑥+3
  • E𝑦=3𝑥2

Q9:

Use technology to plot the graph of 𝑓(𝑥)=2𝑥+5𝑥+5𝑥+2, and use this graph to find the number of real solutions to the equation 2𝑥5𝑥5𝑥=2.

Q10:

If the graph of the function 𝑓(𝑥)=12𝑥+𝑥2𝑥3 is as shown, use this graph to choose the best solution to the equation 𝑥+2𝑥=4𝑥+6.

  • A𝑥=1.866, 1.211, 2.655
  • B𝑥=1.866, 1.211, 2.655
  • C𝑥=1.866, 1.211, 2.655
  • D𝑥=1.866, 1.211, 2.655
  • E𝑥=1.866, 1.211, 2.655

Practice Means Progress

Download the Nagwa Practice app to access questions, unit-exams, and flashcards for your school courses.

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.