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