Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring – it’s a short cut. Use it if you can 2. Using the Quadratic.

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Presentation transcript:

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring – it’s a short cut. Use it if you can 2. Using the Quadratic formula - based on the basic form for a quadratic equation Quadratic Formula

Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for If I factor :

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for If I factor : Set each expression = 0 and solve for “x”

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for a = 1 b = 7 c = 12 Find a, b, and c and substitute into the formula…

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for a = 1 b = 7 c = 12 Evaluate and perform order of operations…

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for a = 1 b = 7 c = 12

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for You can’t factor this, so you MUST use the formula…

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Find a, b, and c and substitute… a = 1 b = - 5 c = - 26

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Evaluate… a = 1 b = - 5 c = - 26

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Since there is no square root of 129 OR any perfect squares to factor out, leave the answer in this form… a = 1 b = - 5 c = - 26

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for You can’t factor this, so you MUST use the formula…

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Find a, b, and c and substitute… a = 3 b = - 7 c = 14

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for WAIT !!! There is a negative sign UNDER the radical. Since that is UNDEFINED, there are NO SOLUTIONS… a = 3 b = - 7 c = 14

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Difference of 2

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Difference of 2 Split middle term

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Cut in half

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Common terms

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Middle two become 1 st binomial

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Divide to get 2 nd binomial

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for Used rule…

Quadratic Formula Finding solutions to quadratic equations can be done in two ways : 1. Factoring 2. Using the Quadratic formula Example : Find the solutions for a = 8 b = - 2 c = - 3

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 FOILed ( n +1 ) 2

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Combined n 2 and moved 85…

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Combined + 1 and (– 85)…

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Divide all terms by 2…

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Factor…

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Solve for “x”…

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Looking for a positive pair, so +6 and +7…

Quadratic Formula – Word problems Use keywords to get the phrasing into an equation… Sum, difference, even, odd, consecutive, squares… EXAMPLE :Find two consecutive positive integers whose sum of squares = 85 Looking for a positive pair, so +6 and +7… CHECK