10.4 Factoring to solve Quadratics. 10.4 – Factoring to solve Quad. Goals / “I can…”  Solve quadratic equations by factoring.

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Presentation transcript:

10.4 Factoring to solve Quadratics

10.4 – Factoring to solve Quad. Goals / “I can…”  Solve quadratic equations by factoring

10.4 – Factoring to solve Quad. So far we’ve found 2 ways to solve quadratic functions  Graphing  Square Roots

y = x 2 – 4x – 5 Solutions are -1 and – Factoring to solve Quad.

Solve 4z 2 = 9. SOLUTION 4z 2 = 9 Write original equation. z 2 = 9 4 Divide each side by 4. Take square roots of each side. z = ±  Simplify – Factoring to solve Quad.

Example 1Example 2 x 2 = 49 (x + 3) 2 = 25 x = ± 7 x + 3 = ± 5 x + 3 = 5 x + 3 = –5 x = 2 x = –8 Example 3 x 2 – 5x + 11 = 0 This equation is not written in the correct form to use this method – Factoring to solve Quad.

If I have 2 numbers and multiply them together, and the product is zero, what are the two numbers?

10.4 – Factoring to solve Quad. One of them must be zero.

10.4 – Factoring to solve Quad. Zero Product Property – For every real number a and b, if ab = 0 then a = 0 or b = 0.

10.4 – Factoring to solve Quad. So if I have (x + 4)(x + 5) = 0 then either (x+ 4) = 0 or (x + 5) = 0

Example 1 x 2 – 2x – 24 = 0 (x + 4)(x – 6) = 0 x + 4 = 0 x – 6 = 0 x = –4 x = 6 Example 2 x 2 – 8x + 11 = 0 x 2 – 8x + 11 is prime; therefore, another method must be used to solve this equation – Factoring to solve Quad.

Example: Given the equation, find the solutions (zeros) (x + 7)(x – 4) = 0(2x + 3)(6x – 8) = 0

10.4 – Factoring to solve Quad. So, if you have a trinomial equal to zero, you can factor it to find the zeros.

10.4 – Factoring to solve Quad. Example: x + x – 42 = 03x – 2x = 21 22

10.4 – Factoring to solve Quad. Story Problem: Suppose that a box has a base with a width of x, a length of x + 2 and a height of 3. It is cut from a square sheet of material with an area of 130 in. Find the dimensions of the box. 2

10.4 – Factoring to solve Quad. What we have is this: 3 3 x + 2 x