All quadratics can be expressed in the form a(x – h)² + k.For example, x? – 4x – 5 = (x – 2)² – 9How to do it:a(x – h)² + k = a[(x – h)(x – h)] + k = a[x² – hx – hx + h²] + k= ax? – 2ahx + ah² + kSo, we want to express x? – 4x – 5 in form a(x – h)² + kx² – 4x – 5 = a(x – h)² + kx2 – 4x – 5 = ax² – 2ahx + ah² + kNow equate the coefficients:1 = a-4 = -2ah - 4 = -2(1)hTherefore, h = 2-5 = h2 + k- 5 = 4 + kTherefore, k = -9Sox² – 4x – 5 = (x – 2)² – 9 Practice the technique with the following quadratics:(i)х2 — 8х + 7(ii)2x2 — 5х + 1(iii)3x2 – x – 4

we have to represent given quadratic equations in the form a(x-h)2+k

Answered: Practice the technique with the…

Math

Advanced Math

Practice the technique with the following quadratics: (i) x? – 8x + 7 (ii) 2x2 – 5x + 1 (iii) Зx? — х — 4

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

4 For the following quadratic, identify the a,b, and c values: 2x² – 3x - 5 a = b = C =
(d) (i) Factorise the quadratic expression x² + 3x - 28. (ii) Use your answer to part (d) (i) to solve the quadratic equation x² + 3x - 28= 0, showing each step in your reasoning. Check that your solution is correct. (e) A student writes down the following piece of work, which contains an error in the reasoning. The equation is: Add 19y to each side: y²-19y=0 y² = 19y y = 19 Divide each side By y: (i) Substitute y = 19 into the left-hand side of the equation y²-19y = 0, and explain why this shows that y = 19 is indeed a solution of the equation. (ii) Write out a complete solution of the equation y2 - 19y = 0. (iii) Explain, as if directly to the student, why their solution is inadequate. (f) Solve the following equation, checking that your solution is correct: 24 72 = 9 <- x+3
Identify a of the following quadratic equation: y = -3x² + 9x – 6 Previous Next MOO
Find the nature of the quadratic form 2x?+2y?+2z?+2yz.
Complete the square to find the solutions of x2 + 8x – 20 = 0 -
. Solve the quadratic equations. (a) 16x² = 81 (b) 2x? + 3x = 2 (c) x² = x - 3 (d) 2r = 3x + 4
Which product is not a difference of two squares? A. (x- 3y)(x+ 3y) B. (x+3y)(3y +x) (-x+3y)(x+3y) d. (x – 3y)(-x -3y) С.
Directions: Complete the following rules. 1. Difference of Squares: (a? - 62 =C %3D 2. Sum of Cubes: a + b³ = %3D 3. Difference of Cubes: a³ – b³ = - 4. How can you tell if you have complet- Directions: Factor each polynomial co 5. x* - 36