Roots are where . The turning point is the minimum or maximum.
The axis of symmetry is the vertical line through the turning point.
A positive coefficient opens upwards; a negative coefficient opens downwards.
Example 1
Sketch the quadratic, marking its roots and turning point.
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Example 2
Sketch the quadratic, marking its roots and turning point.
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Your turn
Question 1
Sketch the quadratic, marking its roots and turning point.
Check answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Question 2
Sketch the quadratic, marking its roots and turning point.
Check answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Question 3
Sketch the quadratic, marking its roots and turning point.
Check answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Question 4
Sketch the quadratic, marking its roots and turning point.
Check answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Question 5
Sketch the quadratic, marking its roots and turning point.
Check answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Sketch the quadratic, marking its roots and turning point.
Answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Sketch the quadratic, marking its roots and turning point.
Answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Sketch the quadratic, marking its roots and turning point.
Answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Sketch the quadratic, marking its roots and turning point.
Answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.
Roots , ; turning point .
Sketch the quadratic, marking its roots and turning point.
Answer
Set each factor equal to zero to find the roots.The axis lies halfway between the roots.Substitute this -value to find the turning point.The coefficient of decides whether the parabola opens upwards or downwards.