8-3A Factoring Trinomials and Solving Quadratic Equations

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8-3A Factoring Trinomials and Solving Quadratic Equations There are numerous methods to factor trinomials. The method used in this presentation is NOT in your textbook. Please pay attention as this method is easier to use than the method presented in the book! Algebra 1 Glencoe McGraw-Hill Linda Stamper

In the previous lesson, you solved a quadratic equation by factoring. The problem. Set each factor equal to zero and solve! The factors were given information. Today you will need to find the factors of a quadratic trinomial and then use the factors to solve a quadratic equation.

Quadratic expressions are written in the following way: trinomial leading coefficient Today we will factor trinomials when the leading coefficient is 1. The coefficient of is 1.

When the coefficient of is 1. becomes (a = 1). Product ac ac b Sum b To factor the trinomial we will. Multiply a times c and place this on top. And place b in the bottom. To fill in the sides of the x you must find two numbers that have a product of ac and a sum of b.

Multiply a times c to find the product. 15 8 5 3 Factor. Multiply a times c to find the product. 15 Draw an X on your paper. 8 5 3 b in the bottom represents the sum To fill in the sides of the x you must find two numbers that have a product of 15 and a sum of 8. This quadratic trinomial is an expression. How do you know it is NOT and equation? Place the values from the sides of the X figure into your factors. Check by doing FOIL in your head! You know there will be an x in each factor! You know there will be an x in each factor!

Multiply a times c to find the product. –2 –3 1 All of today’s problems involving quadratic trinomials will have a leading coefficient of 1. –3 Multiply a times c to find the product. –2 –3 1 b in the bottom represents the sum To fill in the sides of the x you must find two numbers that have a product of –3 and a sum of –2. Place the values from the sides of the X figure into your factors. Check by doing FOIL in your head! You know there will be an x in each factor! You know there will be an x in each factor!

Check by doing FOIL in your head! Example 1 Factor. 12 1. Write the problem. +4 4 +3 2. Draw an X next to the problem. 3 7 3. Multiply a times c to find the product. 4. Write b in the bottom to represent the sum. 5. Fill in the sides of the x by finding two numbers that have a product of the top number and a sum of the bottom number. Check by doing FOIL in your head! 6. Using the values from the sides of the X figure write the factors. Your factors must be in parentheses!

-1 and -3 are the x-intercepts (roots, zeros or solutions of Solve. x + 1 = 0 or x + 3 = 0 - 1 -1 or - 3 -3 x = -1 or x = - 3 -1 and -3 are the x-intercepts (roots, zeros or solutions of the quadratic function: Recall that to find the x-intercepts, you let y = 0. You do the same for a quadratic function. This will graph a PARABOLA!

a>0 so parabola opens up Let x = 0 Quadratic Function y = ax2 + bx + c Quadratic Equation ax2 + bx + c = 0 Axis of symmetry y-intercept (0,3) x = = -4 = -2 2(1) ( 0, c ) x-intercept’s Let y = 0 Factor and solve -1, -3 Vertex ( , y) (x +1) (x + 3) = 0 (-2, -1) a= 1 b= 4 c= 3 a>0 so parabola opens up Vertex : at the vertex, x=-2 Substitute x=-2 into the quadratic function Vertex = (-2, -1) y = (-2)2 + 4(-2) + 3 = -1 Vertex = (-2, -1)

Homework 8-A6 Page 438 # 12–31.