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Lesson: Solving Quadratics Graphically

Sample Question Videos

Worksheet • 8 Questions • 2 Videos

Q1:

Consider the equation 𝑦 = π‘₯ βˆ’ 3 π‘₯ βˆ’ 1 0  .

Find the solutions when 𝑦 = 0 .

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

Find the solutions when 𝑓 ( π‘₯ ) = βˆ’ 6 .

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

Find the solutions when 𝑓 ( π‘₯ ) = βˆ’ 1 0 .

  • A ( 0 , 0 ) , ( 3 , 0 )
  • B ( 2 , 0 ) , ( 5 , 0 )
  • C ( βˆ’ 3 , 0 ) , ( 0 , 0 )
  • D ( βˆ’ 5 , 0 ) , ( 2 , 0 )
  • E ( βˆ’ 2 , 0 ) , ( 5 , 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 curve.
  • BThey will lie on the π‘₯ -axis.
  • CThey will lie in the same quadrant.
  • DThey will not lie on the curve.
  • EThey will not lie in the same quadrant.

Q2:

Work out the coordinates that satisfy the equation 𝑦 = π‘₯ + 4 π‘₯ βˆ’ 5 2 for the given values of 𝑦 .

𝑦 = 7 .

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

𝑦 = 0 .

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

𝑦 = βˆ’ 5 .

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

𝑦 = βˆ’ 9 .

  • A ( βˆ’ 2 , βˆ’ 9 )
  • B ( βˆ’ 5 , βˆ’ 9 )
  • C ( 4 , βˆ’ 9 )
  • D ( 2 , βˆ’ 9 )
  • E ( βˆ’ 4 , βˆ’ 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 lie on the curve.
  • BThey will lie on the π‘₯ -axis.
  • CThey will lie in the same quadrant.
  • DThey will not lie on the curve.
  • EThey will not lie in the same quadrant.

Q3:

If the graph of the quadratic function 𝑓 cuts the π‘₯ -axis at the points ( βˆ’ 3 , 0 ) and ( βˆ’ 9 , 0 ) , what is the solution set of 𝑓 ( π‘₯ ) = 0 in ℝ ?

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

Q4:

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

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

Q5:

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 ( π‘₯ ) = 0 ?

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

Q6:

The diagram shows the graph of 𝑦 = 𝑓 ( π‘₯ ) . What is the solution set of the equation 𝑓 ( π‘₯ ) = 0 ?

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

Q7:

The diagram shows the graph of 𝑦 = 𝑓 ( π‘₯ ) . What is the solution set of the equation 𝑓 ( π‘₯ ) = 0 ?

  • A { βˆ’ 1 }
  • B βˆ…
  • C { βˆ’ 1 , 1 }
  • D { 9 }
  • E { 4 }

Q8:

Consider the equation 𝑦 = π‘₯ βˆ’ 5 π‘₯ + 3 2 . In the following, find a solution by filling the blank space.

( 2 , ) .

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

( βˆ’ 1 , ) .

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

( 0 , ) .

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

( 4 , ) .

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

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

  • AThey will lie on the curve.
  • BThey will lie on the π‘₯ -axis.
  • CThey will lie in the same quadrant.
  • DThey will not lie on the curve.
  • EThey will not lie in the same quadrant.
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