Worksheet: Solving Quadratics Graphically

In this worksheet, we will practice solving quadratic equations by graphing.

Q1:

Consider the graph:

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

  • A 1 2
  • B1 and 3
  • C 1 2 and 3 2 and 3
  • D 1 2 and 3 2
  • 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 { 4 }
  • B { 2 , 2 }
  • C { 9 }
  • D { 2 }
  • E

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

Q4:

Solve 𝑥 𝑥 6 = 0 2 by factoring, and hence determine which of the following figures would be a sketch of 𝑦 = 𝑥 𝑥 6 2 .

  • 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 ( , 4 ]
  • B { 4 }
  • C
  • D { 2 , 2 }

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 { 0 }
  • B { 9 , 9 }
  • C { 0 , 9 }
  • D { 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 { 1 , 0 }
  • B { 4 , 0 }
  • C { 4 , 1 }
  • D { 4 , 1 }
  • E { 4 , 0 }

Q8:

Consider the equation 𝑦 = 𝑥 5 𝑥 + 3 2 . In the following, find a solution by filling the blank space.

( 2 , ) .

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

( 1 , ) .

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

( 0 , ) .

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

( 4 , ) .

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

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 in the same quadrant.
  • DThey will lie on the curve.
  • EThey will lie on the 𝑥 -axis.

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