Solve quadratic equations using the: QUADRATIC FORMULA

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Presentation transcript:

Solve quadratic equations using the: QUADRATIC FORMULA

You will learn 5 different ways to solve a quadratic equations. Solve by graphing Solve by factoring Solve using square roots Solve by completing the square Solve by the quadratic formula

QUADRATIC FORMULA You mainly use the when you have a trinomial equation that you cannot factor!!

2a Quadratic Formula: x = -b + √ b² - 4ac for ax² + bx + c = 0 PARENTHESIS!!!!! Quadratic Formula: x = -b + √ b² - 4ac 2a for ax² + bx + c = 0 This is on your formula sheet.

Quadratic equations can have: Two distinct solutions. One distinct solution. No real solutions.

In order to figure out how many solutions a problem has we will find the discriminant. Aka – The number under the radical. Discriminant : b2 – 4ac

If the discriminant is… Positive – 2 solutions Because the square root of a positive number always has 2 answers. Zero – One solution Because the square root of 0 is 0 and only 0. Negative – No solution Because you cannot take the square root of a negative number.

There are no real solutions There are two real solutions Find the number of solutions of each equation using the discriminant. 1) 3x2 – 2x + 2 = 0 2) 2x2 + 11x + 12 = 0 There are no real solutions There are two real solutions

There is one real solution There are two real solutions Find the number of solutions of each equation using the discriminant. 3) x2 + 8x + 16 = 0 4) x2 – 9x + 4 = 0 There is one real solution There are two real solutions

Steps: Solve using the quadratic equation. Get all the terms to one side of the equals sign. The other side should equal zero. Find: a, b, and c. Plug in a, b, and c to the formula. USE PARENTHESIS!!!!! Simplify piece by piece. If you plug in all at once you will make a mistake.

Solve each equation by using the quadratic formula. 5.) x² – 7x +3 = 0

Solve each equation by using the quadratic formula. 6.) 3x² + 2x –3 = 0

Solve each equation by using the quadratic formula. 7.) 14 = 12 – 5x – x2

Solve each equation by using the quadratic formula. 8) x2 + 4x = -1

Solve each equation by using the quadratic formula. 9)

Solve each equation by using the quadratic formula. 10)