Quadratic Equations

• -4
• -2
• 4
• 2
• 6
• 8
• -6
• -8
• 1
• -1

Answer explanation

Using the Null Factor Law:

1. 1. Factorise the quadratic equation to get two sets of brackets.

2. Remember, you are looking for two factors of the end value that also add to the middle value.

2. 2. Solve each bracket separately, to find each value of x.

3. Once you have solved for the values of x, these will be the x-intercepts of the quadratic equation.

An example is provided in the picture.

• -4
• -2
• 4
• 2
• -8
• 8
• 1
• -1
• 7
• -7

Answer explanation

Using the Null Factor Law:

1. 1. Factorise the quadratic equation to get two sets of brackets.

2. Remember, you are looking for two factors of the end value that also add to the middle value.

2. 2. Solve each bracket separately, to find each value of x.

3. Once you have solved for the values of x, these will be the x-intercepts of the quadratic equation.

An example is provided in the picture.

• -5
• 5
• -3
• -8
• 8
• 15
• -15
• 7
• -7
• 3

Answer explanation

Using the Null Factor Law:

1. 1. Factorise the quadratic equation to get two sets of brackets.

2. Remember, you are looking for two factors of the end value that also add to the middle value.

2. 2. Solve each bracket separately, to find each value of x.

3. Once you have solved for the values of x, these will be the x-intercepts of the quadratic equation.

An example is provided in the picture.

• 3.5
• -1.5
• 1.5
• -16
• 16
• 1
• -1
• 7
• -7
• -3.5

Answer explanation

• 2
• 0.5
• -3
• 3
• 1
• -1
• 2.5
• -2.5
• -2
• -0.5

Answer explanation

• 0.67
• -5
• 5
• 1.5
• -1.5
• 2.5
• -2.5
• -0.67
• 3
• -3

Answer explanation

• (4,-4)
• (-4,4)
• (4,4)
• (6,2)
• (6,0)
• (2,0)
• (4,0)

Answer explanation

Find Turning Point:

1. 1. Find the x-intercepts.

2. 2. Turning point x-coordinate is halfway between the two x-intercepts. So, add the two x-intercepts and divide by two. This will give you the x-coordinate of the turning point.

3. 3. To find the y-coordinate of the turning point, substitute the x-coordinate you just found into the original equation for x and solve.

An example is provided in the picture.

• (3,-25)
• (25,-3)
• (3,0)
• (8,-2)
• (8,0)
• (-2,0)
• (-3,25)

Answer explanation

Find Turning Point:

1. 1. Find the x-intercepts.

2. 2. Turning point x-coordinate is halfway between the two x-intercepts. So, add the two x-intercepts and divide by two. This will give you the x-coordinate of the turning point.

3. 3. To find the y-coordinate of the turning point, substitute the x-coordinate you just found into the original equation for x and solve.

An example is provided in the picture.

• 
• 
• 

Answer explanation

To sketch a quadratic equation, you must work out the:

• - y-intercept

• - x-intercept(s)

• - turning point coordinates

See the steps taken in the photo as an example.

• 
• 
• 

Answer explanation

To sketch a quadratic equation, you must work out the:

• - y-intercept

• - x-intercept(s)

• - turning point coordinates

See the steps taken in the photo as an example.