Worksheet: Equation of a Quadratic Graph

In this worksheet, we will practice identifying the equation of a quadratic by considering its coefficients and relating how they affect the curve.

Q1:

Which of the following graphs represents 𝑓 ( 𝑥 ) = 𝑥 + 1 ?

  • A(c)
  • B(b)
  • C(d)
  • D(a)

Q2:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = 𝑥 1
  • B 𝑦 = 𝑥
  • C 𝑦 = ( 𝑥 + 1 )
  • D 𝑦 = 𝑥
  • E 𝑦 = ( 𝑥 1 )

Q3:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = 𝑥 1
  • B 𝑦 = 𝑥
  • C 𝑦 = ( 𝑥 + 1 )
  • D 𝑦 = 𝑥
  • E 𝑦 = ( 𝑥 1 )

Q4:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = ( 𝑥 + 3 )
  • B 𝑦 = 𝑥 3
  • C 𝑦 = 𝑥 + 3
  • D 𝑦 = ( 𝑥 3 )
  • E 𝑦 = 𝑥 ( 𝑥 3 )

Q5:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = ( 𝑥 + 1 )
  • B 𝑦 = 𝑥 1
  • C 𝑦 = ( 𝑥 1 )
  • D 𝑦 = 𝑥 + 1
  • E 𝑦 = 1 𝑥

Q6:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = ( 𝑥 + 7 )
  • B 𝑦 = 𝑥 + 7
  • C 𝑦 = ( 𝑥 7 )
  • D 𝑦 = ( 𝑥 + 7 )
  • E 𝑦 = 𝑥 ( 𝑥 + 7 )

Q7:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = ( 𝑥 1 ) 5
  • B 𝑦 = ( 𝑥 + 5 ) 1
  • C 𝑦 = ( 𝑥 5 ) ( 𝑥 1 )
  • D 𝑦 = ( 𝑥 5 ) 1
  • E 𝑦 = ( 𝑥 + 5 ) ( 𝑥 + 1 )

Q8:

Write the quadratic equation represented by the graph shown.

  • A 𝑦 = ( 𝑥 + 1 ) + 3
  • B 𝑦 = ( 𝑥 1 ) + 3
  • C 𝑦 = ( 𝑥 1 ) ( 𝑥 + 1 )
  • D 𝑦 = ( 𝑥 1 ) + 3
  • E 𝑦 = ( 𝑥 1 ) ( 𝑥 + 3 )

Q9:

Write the quadratic equation represented by the graph shown. Give your answer in standard form.

  • A 𝑦 = 𝑥 1 0 𝑥 1 6
  • B 𝑦 = 𝑥 6 𝑥 1 6
  • C 𝑦 = 𝑥 + 1 0 𝑥 + 1 6
  • D 𝑦 = 𝑥 + 6 𝑥 1 6
  • E 𝑦 = 𝑥 1 0 𝑥 + 1 6

Q10:

Write the quadratic equation represented by the graph shown. Give your answer in standard form.

  • A 𝑦 = 𝑥 + 7 𝑥 + 3 0
  • B 𝑦 = 𝑥 + 7 𝑥 3 0
  • C 𝑦 = 𝑥 1 3 𝑥 + 3 0
  • D 𝑦 = 𝑥 7 𝑥 + 3 0
  • E 𝑦 = 𝑥 1 3 𝑥 + 3 0

Q11:

Write the quadratic equation represented by the graph shown. Give your answer in standard form.

  • A 𝑦 = 4 𝑥 4 𝑥 + 1 5
  • B 𝑦 = 4 𝑥 4 𝑥 1 5
  • C 𝑦 = 4 𝑥 1 6 𝑥 + 1 5
  • D 𝑦 = 4 𝑥 + 4 𝑥 1 5
  • E 𝑦 = 4 𝑥 1 6 𝑥 + 1 5

Q12:

Write the quadratic equation represented by the graph shown. Give your answer in standard form.

  • A 𝑦 = ( 𝑥 + 6 ) + 3
  • B 𝑦 = ( 𝑥 6 ) + 3
  • C 𝑦 = ( 𝑥 6 ) ( 𝑥 + 3 )
  • D 𝑦 = ( 𝑥 6 ) + 3
  • E 𝑦 = ( 𝑥 6 ) ( 𝑥 + 3 )

Q13:

Write the quadratic equation represented by the graph shown. Give your answer in factored form.

  • A 𝑦 = 𝑥 ( 𝑥 + 5 )
  • B 𝑦 = 𝑥 ( 𝑥 5 )
  • C 𝑦 = 𝑥 ( 𝑥 + 5 )
  • D 𝑦 = 𝑥 ( 𝑥 5 )
  • E 𝑦 = ( 𝑥 9 )

Q14:

Write the quadratic equation represented by the graph shown. Give your answer in factored form.

  • A 𝑦 = ( 𝑥 + 2 ) ( 𝑥 4 )
  • B 𝑦 = ( 𝑥 2 ) ( 𝑥 + 4 )
  • C 𝑦 = ( 𝑥 2 ) ( 𝑥 + 4 )
  • D 𝑦 = ( 𝑥 + 2 ) ( 𝑥 4 )
  • E 𝑦 = ( 𝑥 + 2 ) ( 𝑥 + 4 )

Q15:

Write the quadratic equation represented by the graph shown. Give your answer in factored form.

  • A 𝑦 = ( 𝑥 + 5 ) ( 𝑥 2 )
  • B 𝑦 = ( 𝑥 5 ) ( 𝑥 + 2 )
  • C 𝑦 = ( 𝑥 5 ) ( 𝑥 + 2 )
  • D 𝑦 = ( 𝑥 + 5 ) ( 𝑥 2 )
  • E 𝑦 = ( 𝑥 5 ) ( 𝑥 2 )

Q16:

The point ( 𝑎 6 , 0 ) is the vertex of the graph of the quadratic function 𝑓 . If the solution set of the equation 𝑓 ( 𝑥 ) = 0 is { 5 } , what is the value of 𝑎 ?

Q17:

Given that the point ( 4 , 4 ) is the vertex of the graph of the quadratic function 𝑓 , and 6 is a root of the equation 𝑓 ( 𝑥 ) = 0 , find the other root of the equation.

Q18:

Which of the following graphs represents the equation 𝑦 = 𝑥 5 𝑥 + 8 ?

  • A
  • B
  • C
  • D