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**5.6 Quadratic Formula & Discriminant**

OBJ: To find the discriminant & tell how many (and what type) of solutions there are & to a quadratic equation solve quadratic equations using the quadratic formula & use the quadratic formula in real-life situations 5.6 Quadratic Formula & Discriminant Do Now:

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Discriminant b2 - 4ac The discriminant tells you how many solutions and what type you will have. If it is: positive, there are 2 real solutions negative, there are 2 imaginary solutions zero, there is 1 real solution

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**Ex 1: 9x2+6x-4=0 a=9, b=6, c=-4 b2-4ac=(6)2-4(9)(-4) =36+144=180**

2 real solutions c. 9x2+6x+5=0 a=9, b=6, c=5 b2-4ac=(6)2-4(9)(5) =36-180=-144 2 imaginary solutions Find the discriminant and give the number and type of solutions. 9x2+6x+1=0 a=9, b=6, c=1 b2-4ac=(6)2-4(9)(1) =36-36=0 1 real solution

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Quadratic Formula Use the quadratic formula when you can’t factor to solve a quadratic equation. (or when you’re stuck on how to factor the equation)

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Ex 2: a. 3x2+8x=35 3x2+8x-35=0 a=3, b=8, c= -35 OR

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b. -2x2=-2x+3 -2x2+2x-3=0 a=-2, b=2, c= -3

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