Solving Quadratics by Completing the Square

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Presentation transcript:

Solving Quadratics by Completing the Square 9.4 Day 1 Solving Quadratics by Completing the Square

Warm-Up Factor the following: 1. 𝑥 2 +20𝑥+100 2. 𝑥 2 −18𝑥+81 3. 𝑥 2 −4𝑥+4

Completing the Square Steps to solving a quadratic equation by completing the square: 1. Get the equation in the form 𝑎𝑥 2 +𝑏𝑥 ______=𝑐 ______. (Move the c value to the other side, leaving blanks as shown above) 2. To fill in the blanks: Divide the b value by and ____________ it. 3. the perfect square trinomial 4. the equation for x using square roots

Example 1 a) Find the value of c that makes x2 – 12x + c a perfect square trinomial. b) Find the value of c that makes x2 + 14x + c a perfect square trinomial.

Example 2 Solve the quadratic equations using completing the square. A. 𝑥 2 +10𝑥−3=0 B. 𝑥 2 −6𝑥−8=0

Example 2 cont. C. 𝑥 2 +6𝑥+5=12

If the Coefficient is not 1…. If the coefficient of x2 is not 1…we have to do one extra step! FIRST: each side of the equation by the of x2

Example 3 a) 3x2 – 6x – 12 = 0 b) 5x2 – 10x + 30 = 0

Example 3 cont. c) –2x2 + 36x – 10 = 24