Lesson 2.3 - Algebra of Quadratic Relations Functions & Trig Santowski.

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Lesson Algebra of Quadratic Relations Functions & Trig Santowski

REVIEW Lesson 1 focused on Quadratic Relations from the view point of generating tables of values and then graphing the scatter plots Lesson 2 focussed on looking at the graphs of quadratic relations (called parabolas) and seeing 5 key features: (1) axis of symmetry (2) vertex (3) roots (or zeroes or x-intercepts) (4) y-intercepts (5) direction of opening

Lesson Objectives In lesson 3, we will focus on: (1) review factoring skills (to convert standard form into intercept form) (2) review the method of completing the square (to convert standard form into vertex form) (3) solve quadratic equations using (a) factoring methods, (b) completing the square and (c) the quadratic formula

(A) Factoring Trinomials We will focus on changing quadratic equations from standard form (ax 2 + bx + c) to intercept form (a(x - R 1 )(x - R 2 )) by factoring (i) x 2 - 3x - 10 (ii) x (iii) 2x 2 + 5x - 3 (iv)12x 2 - 7x - 5

(B) Completing the Square We will focus on changing quadratic equations from standard form (ax 2 + bx + c) to vertex form (a(x - h) 2 + k) by completing the square (i) x 2 - 4x - 10 (ii) x 2 - 3x + 1 (iii) 2x 2 + 6x - 1 (iv) 3x 2 - 7x + 2

(C) Solving Q/E by Factoring We will now take a quadratic equation and factor it in order to solve for x (ii) (x - 3)(x + 7) = 0 (ii) x 2 - x - 2= 0 (iii) 4x 2 + 4x - 15 = 0 (iv) 4x = 0

(D) Solving Q/E by Completing the Square We will now take a quadratic equation and complete the square in order to isolate the x and thereby solve for x (i) 2(x - 5) = 0 (ii) x 2 - 6x - 16 = 0 (iii) 3x 2 - 6x - 8 = 0

(E) Solving Q/E by Quadratic Formula We will now take a quadratic equation and keep it in standard form and simply use the quadratic formula to solve (i) 2x 2 + 5x - 7 = 0 (ii) -5x 2 - x + 9 = 0

(F) Solving Q/E by the most appropriate method Since you have 3 different methods, you must occasionally decide which method works best depending on the presentation of the equation (i) x 2 - 5x + 6 = 0 (ii) x = 8x (iii) 4x 2 + 7x = -8