tag:blogger.com,1999:blog-2490105929626066237.post4327137992095735054..comments2024-03-18T01:07:22.187-07:00Comments on The Math Blog: How to convert a quadratic equation to intercept formUnknownnoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2490105929626066237.post-53006380912133673752014-11-19T09:22:37.946-08:002014-11-19T09:22:37.946-08:00We can convert a quadratic function, in standard f...We can convert a quadratic function, in standard form y = ax^2 + bx + c, into the intercept form.<br />y = a*(x - x1)(x - x2)<br />y = a*(x^2 + bx/a + c/a) (1)<br />Recall the development of the quadratic formula:<br />x^2 + bx/a + c/a + (b^2/4a^2 - b^2/4a^2) = 0<br />(x + b/2a)^2 - (b^2 - 4ac)/4a^2 = (x + b/2a)^2 - d^2/4a^2. (2)<br />Call d^2 = b^2 - 4ac. Replace this expression (2) into (1), we get the quadratic function written in intercept form:<br />y = a*(x + b/2a + d/2a)(x + b/2a - d/2a) (3) with d^2 = b^2 - 4ac.<br />From this form, we deduct the Quadratic Formula in Intercept Form:<br /><br />x = -b/2a + (or -) d/2a. (4)<br /><br />In this formula:<br />- the quantity (-b/2a) represents the x-coordinate of the parabola axis.<br />- The 2 quantities (-d/2a) and (d/2a) represent the 2 equal distances from the axis to the two x-intercepts.<br />- If d = 0, there is double root at x = -b/2a.<br />- If d^2 > 0, There are 2 real roots (2 x-intercepts)<br />- If d^2 < 0, there are no intercepts. There are 2 complex roots.Anonymoushttps://www.blogger.com/profile/12817209010795253316noreply@blogger.comtag:blogger.com,1999:blog-2490105929626066237.post-44996095523011770602012-01-02T12:13:29.661-08:002012-01-02T12:13:29.661-08:00Thank you sooo much, our teacher gave us problems ...Thank you sooo much, our teacher gave us problems like these for hw over winterbreak w/o teaching us how to do it and we have a test the day we get back!Anonymousnoreply@blogger.com