4D - The general quadratic formula

Learning intentions:

In this section we will examine:

    • The general quadratic formula
    • The axis of symmetry

The general quadratic formula

When quadratic equations become more complex, factorisation and using the null factor law to solve becomes a long and arduous process. However, the general quadratic formula can be easily applied to solve these problems.

  • When the equation is in the general form (ax2 + bx + c = 0), the general quadratic formula can be used to solve for x, The general quadratic formula states:
  • To use the formula, simply substitute the coefficients that correspond to a, b and c in the general quadratic equation (ax2 + bx + c = 0).

4D - VIDEO EXAMPLE 1:

Use the general quadratic formula to solve the following equation for x:

4D - VIDEO EXAMPLE 2:

Use the general quadratic formula to solve the following equation for x:

4D - VIDEO EXAMPLE 3:

Use the general quadratic formula to solve the following equation for x:

The axis of symmetry

From the general quadratic formula, we can see that the x-intercepts are an equal distance from the the axis of symmetry (which will be explore further in completing the square):

Success criteria:

You will be successful if you can:

    1. Use the general quadratic formula to solve quadratic equations.
    2. Use the axis of symmetry to determine the turning point of a parabola.