6 Example 1 continued𝑥= −4± 4 2𝑥= − 𝑎𝑛𝑑 𝑥= −4−2 2x=-1 and x=-3
7 WHY USE THE QUADRATIC FORMULA? The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it.
8 DefinitionDefinition:Discriminant is the piece under the radical: b2 – 4ac
9 WHY IS THE DISCRIMINANT IMPORTANT? The discriminant tells you the number and types of answers(roots) you will get. The discriminant can be +, –, or 0Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.
10 WHAT THE DISCRIMINANT TELLS YOU! Value of the DiscriminantNature of the SolutionsNegative2 imaginary solutionsZero1 Real SolutionPositive2 Real Solutions
11 Refresh What is an imaginary number? When you have a square root of a negative number.Called i.−1 =𝑖
12 Example with imaginary answer: 𝑥 2 −2𝑥+5=0 Try solving on your own…
13 𝑥 2 −2𝑥+5=0 𝑥= −(−2)± (−2) 2 −4∙1∙5 2∙1 Plug in a,b and c 𝑥= 2± −16 2∙1 Simplify under the radical𝑥= 2±𝑖 Factor out the -1, it becomes i.𝑥= 2±𝑖∙ Take square root𝑥=1+2𝑖 𝑎𝑛𝑑 𝑥=1−2𝑖 Divide by 2.
14 You try! Start with 1 and 4, then go on to the others.
15 Write a quadratic in general from: and the x-intercepts are 5 and 2.What can we do?
16 SolutionWrite it factored form (because that is what information we have.𝑦=(𝑥−5)(𝑥−2)Then foil to get it in general𝑦= 𝑥 2 −7𝑥−10
17 Homework: This is a massive assignment! 7.4 Worksheet1 a-c2 all3 a-f4 a-d5 a-c