Unit 3 - Standard Form
- determine max/min values of a quadratic relation using zeroes and symmetry
- convert a quadratic relation from standard form to vertex form (complete the square)
- solve quadratic equations using the quadratic formula
- solve real-world problems involving max/min
- the value of a gives you the shape and direction of opening
- the value of c is the y-intercept
To get the x-intercepts, solve using the quadratic formula.
The number inside the square root (b² - 4ac) of the quadratic formula is called the Discriminant (D). It helps us tell how many solutions the quadratic equation will have without having to use the whole formula.
When D < 0, there will be no solutions (x-intercepts). When D > 0, there will be 2 solutions. And when D = 0, there will be only 1 solution.
Use the completing the square method to convert standard form into vertex form.
Quadratic Formula Example
Completing the Square Example
Example of a Word Problem
h = -0.25d² + 2d + 1.5, where h is the height and d is the horizontal distance in metres.
- What is the initial height of the basketball?
- What is the maximum height reached by the basketball and at what horizontal distance does this occur at?