Lesson Worksheet: Solving Quadratic Equations Graphically Mathematics

In this worksheet, we will practice solving quadratic equations using function graphs.

Q1:

The curve of a quadratic function, 𝑓, intersects the 𝑥-axis at the points (1,0) and (4,0). What is the solution set of the equation 𝑓(𝑥)=0?

  • A{4,0}
  • B{4,1}
  • C{4,1}
  • D{1,0}
  • E{4,0}

Q2:

If the point (9,0) is the vertex of the graph of the quadratic function 𝑓, what is the solution set of the equation 𝑓(𝑥)=0?

  • A{9,9}
  • B{9}
  • C{0}
  • D{0,9}

Q3:

At which values of 𝑥 does the graph of the equation 𝑦=(𝑥+2)(𝑥6) cross the 𝑥-axis?

  • A4 and 12
  • B4 and 12
  • C4 and 12
  • D2 and 6
  • E2 and 6

Q4:

The diagram shows the graph of 𝑦=𝑓(𝑥). What is the solution set of the equation 𝑓(𝑥)=0?

  • A{2,2}
  • B{2}
  • C{4}
  • D{4,4}
  • E

Q5:

The diagram shows the graph of 𝑦=𝑓(𝑥). What is the solution set of the equation 𝑓(𝑥)=0?

  • A{2}
  • B{9}
  • C
  • D{2,2}
  • E{4}

Q6:

The graph shows the function 𝑓(𝑥)=𝑥2𝑥+3. What is the solution set of 𝑓(𝑥)=0?

  • A{0,2}
  • B{0,3}
  • C{1,3}
  • D{2,3}
  • E

Q7:

By drawing a graph of the function 𝑓(𝑥)=2𝑥3𝑥, find the solution set of 𝑓(𝑥)=0.

  • A0,23
  • B1,23
  • C1,32
  • D0,32
  • E{2,3}

Q8:

Solve 𝑥𝑥6=0 by factoring, and hence determine which of the following figures would be a sketch of 𝑦=𝑥𝑥6.

  • A
  • B
  • C
  • D
  • E

Q9:

The graph shows the function 𝑓(𝑥)=2𝑥4𝑥6.

What is the solution set of 𝑓(𝑥)=0?

  • A{1,3}
  • B{2,3}
  • C{0,6}
  • D{1,3}
  • E{3,1}

What is the solution set of 𝑓(𝑥)=6?

  • A{1,2}
  • B{0,2}
  • C{1}
  • D{0}
  • E{0,2}

Q10:

Using the given graph of the equation 𝑦=𝑥+2𝑥5, find which of the following is the best approximation for the solutions to 𝑥+2𝑥5=0.

  • A𝑥=4 or 2
  • B𝑥=3.5 or 1.5
  • C𝑥=3 or 1

This lesson includes 25 additional questions and 91 additional question variations for subscribers.

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