Worksheet: Solving Quadratic Equations Graphically

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

Q1:

Consider the graph:

The roots of a quadratic can be read from the graph. What are they?

  • A1 and 3
  • B12 and 32 and 3
  • C12
  • D12 and 32
  • E1 and 1

Q2:

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}

Q3:

If the graph of the quadratic function 𝑓 cuts the 𝑥-axis at the points (3,0) and (9,0), what is the solution set of 𝑓(𝑥)=0 in ?

  • A{3,9}
  • B{9,0}
  • C{(3,0)}
  • D{3,9,0}
  • E{(3,9)}

Q4:

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

Q5:

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

  • A
  • B{4}
  • C{2,2}
  • D(,4]

Q6:

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}

Q7:

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}

Q8:

Consider the equation 𝑦=𝑥5𝑥+3. In the following, find a solution by filling the blank space.

(2,).

  • A(2,2)
  • B(2,7)
  • C(2,7)
  • D(2,5)
  • E(2,3)

(1,).

  • A(1,1)
  • B(1,4)
  • C(1,3)
  • D(1,9)
  • E(1,7)

(0,).

  • A(0,2)
  • B(0,5)
  • C(0,5)
  • D(0,3)
  • E(0,3)

(4,).

  • A(4,1)
  • B(4,2)
  • C(4,6)
  • D(4,0)
  • E(4,9)

These solutions (𝑥,𝑦) can be plotted as seen in the figure. What will be true of any other solution plotted in the plane?

  • AThey will not lie on the curve.
  • BThey will not lie in the same quadrant.
  • CThey will lie on the curve.
  • DThey will lie on the 𝑥-axis.
  • EThey will lie in the same quadrant.

Q9:

Solve 𝑥+4𝑥4=0 by factoring, and hence determine which of the following figures would be a sketch of 𝑦=𝑥+4𝑥4.

  • A
  • B
  • C
  • D
  • E

Q10:

Consider the function 𝑓(𝑥)=𝑥3𝑥10.

Find the solutions when 𝑓(𝑥)=0 in the form of (𝑥,𝑦).

  • A(5,0), (2,0)
  • B(1,0), (10,0)
  • C(2,0), (5,0)
  • D(2,0), (5,0)
  • E(5,0), (2,0)

Find the solutions when 𝑓(𝑥)=6 in the form of (𝑥,𝑦).

  • A(4,6), (1,6)
  • B(5,6), (2,6)
  • C(4,6), (1,6)
  • D(2,6), (5,6)
  • E(1,6), (4,6)

Find the solutions when 𝑓(𝑥)=10 in the form of (𝑥,𝑦).

  • A(5,10), (2,10)
  • B(2,10), (5,10)
  • C(0,10), (3,10)
  • D(2,10), (5,10)
  • E(3,10), (0,10)

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution?

  • AThey will lie on the 𝑥-axis.
  • BThey will lie in the same quadrant.
  • CThey will not lie on the curve.
  • DThey will not lie in the same quadrant.
  • EThey will lie on the curve.

Q11:

Work out the coordinates that satisfy the equation 𝑦=𝑥+4𝑥5 for the given values of 𝑦.

𝑦=7.

  • A(6,7), (2,7)
  • B(4,7), (1,7)
  • C(5,7), (1,7)
  • D(1,7), (5,7)
  • E(2,7), (6,7)

𝑦=0.

  • A(1,0), (5,0)
  • B(5,0), (1,0)
  • C(1,0), (5,0)
  • D(5,0), (1,0)
  • E(4,0), (1,0)

𝑦=5.

  • A(5,5), (1,5)
  • B(4,5), (0,5)
  • C(2,5), (2,5)
  • D(0,5), (4,5)
  • E(1,5), (5,5)

𝑦=9.

  • A(4,9)
  • B(2,9)
  • C(5,9)
  • D(2,9)
  • E(4,9)

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution?

  • AThey will not lie on the curve.
  • BThey will not lie in the same quadrant.
  • CThey will lie on the 𝑥-axis.
  • DThey will lie on the curve.
  • EThey will lie in the same quadrant.

Q12:

Solve 𝑥𝑥+6=0 by factoring, and hence determine which of the following figures would be a sketch of 𝑦=𝑥𝑥+6.

  • A
  • B
  • C
  • D
  • E

Q13:

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

Q14:

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}

Q15:

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

Q16:

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}

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