Factored or intercept form of a quadratic is helpful when finding the x-intercepts of a quadratic function. The x-intercepts are happen are when y = 0. If you tried to substitute y = 0 into a quadratic in standard form you can not use traditional methods for solving for x. (0 = x² + 2x - 3) What we can do with certain quadratic functions is re-write them in factored form and use the zero property product rule.
First lets practice finding the x-intercepts in factored form. Watch the video below and copy the examples into your notes. Then complete the skill.
Finding the x-intercepts in Standard Form
By factoring the quadratic you are re-writing it in factored/intercept form. When a quadratic rule is written in factored form you can easily identify the x-intercepts. Just as in standard form, the a value will identify the direction the parabola opens (max/min).
Notice the subtraction signs, this shows a sign change when identifying the x-int. because you are identifying the x value that causes the factor to cancel out to 0.
The example below shows the steps of converting from standard form into factored form in order to find
the zeros.
Notice the subtraction signs, this shows a sign change when identifying the x-int. because you are identifying the x value that causes the factor to cancel out to 0.
The example below shows the steps of converting from standard form into factored form in order to find
the zeros.
Complete the two practice skills below. You only need to watch the video if you need additional support.
Finding the vertex and y-intercept in factored form.
In the previous lesson you reviewed how to find the vertex and y-intercepts in standard form. If a quadratic is written in factored form you could distribute and re-write the quadratic in standard, however it can be quicker to apply other algebraic methods by leaving it in factored form.
Copy the example below into your notes.
Copy the example below into your notes.
Complete the 3 questions from the worksheet linked below, then check you answers.