Quadratic Equation from X Intercept and Two Points

Using the Null Factor Law:

1. 1. Multiply the value in front of $$x^2$$ and number on the end. From this, find two factors of this answer that add to the middle number.

2. 2. Split the middle term into these two factors in front of x

3. 3. Factorise the equation to get two sets of brackets.

2. 4.. 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.

Using the Null Factor Law:

1. 1. Multiply the value in front of $$x^2$$ and number on the end. From this, find two factors of this answer that add to the middle number.

2. 2. Split the middle term into these two factors in front of x

3. 3. Factorise the equation to get two sets of brackets.

2. 4.. 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.

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.

Drag the dots on to the y-intercept and turning point of the quadratic equation.

To calculate the y-intercept, let x=0 and solve.

To calculate the turning point coordinates:

1. 1. You will need to use the quadratic formula to calculate the two x-intercepts

2. 2. Use these x-intercepts to find the x-coordinate of the turning point.

3. 3. Substitute this x-coordinate into the quadratic equation (for x) to find the y-coordinate of the turning point.

Drag the dots on to the y-intercept and turning point of the quadratic equation.

To calculate the y-intercept, let x=0 and solve.

To calculate the turning point coordinates:

1. 1. You will need to use the quadratic formula to calculate the two x-intercepts

2. 2. Use these x-intercepts to find the x-coordinate of the turning point.

3. 3. Substitute this x-coordinate into the quadratic equation (for x) to find the y-coordinate of the turning point.

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.

Discriminant formula:

$$\Delta=b^2-4ac$$

where a, b and c all come from the values in the quadratic equation $$y=ax^2+bx+c$$

So substitute the values of a, b and c into the discriminant formula and calculate.

If $$\Delta<0$$ there are no x-intercepts

If $$\Delta=0$$ there is one x-intercept

If $$\Delta>0$$ there are two x-intercepts

Discriminant formula:

$$\Delta=b^2-4ac$$

where a, b and c all come from the values in the quadratic equation $$y=ax^2+bx+c$$

So substitute the values of a, b and c into the discriminant formula and calculate.

If $$\Delta<0$$ there are no x-intercepts

If $$\Delta=0$$ there is one x-intercept

If $$\Delta>0$$ there are two x-intercepts

Discriminant formula:

$$\Delta=b^2-4ac$$

where a, b and c all come from the values in the quadratic equation $$y=ax^2+bx+c$$

So substitute the values of a, b and c into the discriminant formula and calculate.

If $$\Delta<0$$ there are no x-intercepts

If $$\Delta=0$$ there is one x-intercept

If $$\Delta>0$$ there are two x-intercepts