Section 4 3 Notes Solving Quadratic Equations by

Section 4. 3 Notes: Solving Quadratic Equations by Factoring

Review: Factoring using the Greatest Common Factor (GCF) Example 1: Factor 9 y 2 + 3 y. Example 2: Factor 5 a 2 – 20 a.

Factoring a difference of two squares Pattern: a 2 – b 2 = (a + b)(a – b) Example: x 2 – 9 = (x + 3)(x – 3)

Example 3: Factor 4 x 2 – 25 Example 4: Factor y 2 – 36

Example 5: Factor 3 y 2 – 108 Example 6: Factor 64 x 2 – 121 y 2

Factoring using the Product Sum Method Example 7: Factor x 2 – 2 x – 15. Example 8: Factor x 2 + 14 x + 48.

Example 9: Factor 4 x 2 – 40 x + 84

Steps to Slide and Divide If a ≠ 1: ax 2 + bx + c 1) Multiply a and c. (slide a to c) Example: 2 x 2 + 17 x + 21 2) Rewrite in the form x 2 + bx + (ac) 3) Factor using product sum 4) Divide the numbers by a 5) Reduce fractions 6) Bring the denominator in front of the x.

Example 10: Factor 3 x 2 + 5 x – 2.

Example 11: Factor 10 x 2 + 68 x + 48.

Example 12: Factor 7 x 2 – 32 x – 60.

Solving Quadratic Equations

Example 13: Solve (x + 2)x = 0

Example 14: Solve (x + 3)(x – 4) = 10

Example 15: Solve 5 a 2 – 20 a = 0

Example 16: Solve x 2 – 64 = 0

Example 17: Solve x 2 + 14 x = – 48

Example 18: Find the zeros of 6 x 2 – 5 x – 4 = 0

You can use the FOIL method to write a quadratic equation that is in factored form in standard form. The FOIL Method uses the Distributive Property to multiply binomials.

Example 19: Write a quadratic equation in standard form with and – 5 as its roots.

Example 20: Write a quadratic equation with and 5 as its roots. Write the equation in the form ax 2 + bx + c = 0, where a, b, and c are integers.

Example 21: The entrance to an office building is an arch in the shape of a parabola whose vertex is the height of the arch. The height of the arch is given by h = 9 – x 2, where x is the horizontal distance from the center of the arch. Both h and x are measured in feet. How wide is the arch at ground level?

Example 22: During a match, Andre hit a lob right off the court with the ball traveling in the shape of a parabola whose vertex was the height of the shot. The height of the shot is given by h = 49 – x 2, where x is the horizontal distance from the center of the shot. Both h and x are measured in feet. How far was the lob hit?

Example 23: Find the value of x and the dimensions of the rectangle.

Example 24: Find the value of x and the dimensions of the rectangle.