1 / 13

5.4 Factoring ax 2 + bx +c

5.4 Factoring ax 2 + bx +c. 12/10/2012. In the previous section we learned to factor x 2 + bx + c where a = 1. In this section, we’re going to factor ax 2 + bx + c where a ≠ 1 . Ex: Factor 3x 2 + 7x +2 We’re still going to use the “Big X” Method. The Big “X” method.

winifred-cohen
Download Presentation

5.4 Factoring ax 2 + bx +c

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5.4Factoring ax2 + bx +c 12/10/2012

  2. In the previous section we learned to factor x2 + bx + c where a = 1. In this section, we’re going to factor ax2+ bx + c where a ≠ 1. Ex: Factor 3x2 + 7x +2 We’re still going to use the “Big X” Method.

  3. The Big “X”method Factor: ax2 + bx + c Think of 2 numbers that Multiply to a•cand Add to b multiply a a Simplify like a fraction if needed a•c Simplify like a fraction if needed #1 #2 b add Answer: Write the simplified answers in the 2 ( ). Top # is coefficient of x and bottom # is the 2nd term

  4. Factor: 3x2 + 7x + 2 Think of 2 numbers that Multiply to 6 and Add to 7 6 x 1 = 6 6 + 1 = 7 1 3•2 = 6 3 3 Simplify like a fraction . ÷ by 3 6 1 2 multiply 7 a a a•c #1 #2 b Answer: (1x + 2) (3x + 1) or (x + 2) (3x + 1) add

  5. Checkpoint ANSWER ax2 bx c + + 2. ANSWER ( ) ( ) 2y + 7 y + 1 3. 3r2 8r 5 ANSWER + + 2y2 9y 7 + + ( ( ) ) ( ( ) ) 3r 2x + + 5 1 r x + + 1 5 Factor when c is Positive Factor the expression. 1. 2x2 11x 5 + +

  6. Factor: 4x2-16x -9 Think of 2 numbers that Multiply to -36 and Add to -16 -18 x 2 = -36 -18 + 2 = -16 4(-9) = -36 2 4 4 2 Simplify like a fraction . ÷ by 2 Simplify like a fraction . ÷ by 2 -18 2 1 -9 multiply -16 a a a•c #1 #2 b Answer: (2x -9) (2x + 1) add

  7. Factor: 6x2+27x -15 Do 6, 27 and -15 have any factors in common? Yes, 3. Factor 3 out. 3(2x2+9x –5). Then Factor what’s in the ( ). Think of 2 numbers that Multiply to -10 and Add to 9 -1 x 10 = -10 -1 + 10 = 9 2(-5) = -10 2 2 1 Simplify like a fraction . ÷ by 2 multiply a a -1 10 a•c 5 9 #2 #1 b add Answer: 3(2x - 1) (x + 5) (Don’t forget the 3!!!)

  8. Checkpoint ANSWER ( ) ( ) – 3z 4 2z + 3 5. ANSWER ( ) ( ) 11x + 6 x + 1 11x2 17x 6 + + ax2 + bx + c 6. ANSWER ( ) ( ) – – 2w 1 w 1 4w2 – 6w + 2 2 Factor Factor the expression. 4. – 6z2 + z 12

  9. Finding the Zeros of the Function Is the same as solving ax2+bx+c = 0 Graphically, finding the zeros of the quadratic function means finding the x-intercepts of the parabola.

  10. 4 3 SOLUTION To find the zeros of the function, let Then solve for x. – – x2 x = y Write original function. 3 4 = – – x2 x Let y0. = 0 3 4 – ( 3x4 ) – – x2 x = y 3 4. 0 Factor the right side. = + + ( x 1 x 1 ) or 0 Use the zero product property. = 0 = – 3x4 y 0. – = x 1 Solve for x. = = x Example 4 Find the Zeros of a Quadratic Function Find the zeros of

  11. 4 4 3 3 The zeros of a function are also the x-intercepts of the graph of the function. So, the answer can be checked by graphing The x-intercepts of the graph are and , so the answer is correct. CHECK – – 1 1. – – x2 x = y 3 4. Example 4 Find the Zeros of a Quadratic Function ANSWER The zeros of the function are and

  12. Checkpoint 1 1 1 2 2 3 7. = y – – – + x2 x2 2x 7x 2 3 3 1 ANSWER – , 1 , 3 , 4 8. = y ANSWER 9. – + x2 18x = y 4 8 ANSWER Find the Zeros of a Quadratic Function Find the zeros of the function.

  13. Homework 5.4 p.244 #18-25, 46-48, 57-59

More Related