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
  • B 1 2 and 32 and 3
  • C 1 2
  • D 1 2 and 32
  • E 1 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 ) , ( 1 0 , 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 , 1 0 ) , ( 2 , 1 0 )
  • B ( 2 , 1 0 ) , ( 5 , 1 0 )
  • C ( 0 , 1 0 ) , ( 3 , 1 0 )
  • D ( 2 , 1 0 ) , ( 5 , 1 0 )
  • E ( 3 , 1 0 ) , ( 0 , 1 0 )

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.

  • A 𝑥 = 4 or 2
  • B 𝑥 = 3 . 5 or 1.5
  • C 𝑥 = 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.

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

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