3 QUADRATIC CONGRUENCES

2 4 Quadratic Formula = 2( 3) 5 52 4( 3)(9) a = -3, b = 5, and c = 9 = 6 5 25 108 Multiply = 6 5 133 Add x = 6 5 133 or x = 6 5 133 Separate the solutions 2 8 -1 1 Simplify Check the solutions by using the CALC menu on a graphing calculator to determine the zeros of the related quadratic function To the nearest tenth, the solution set is

11 Rules of Roots - mathucdavisedu

1 2 Quadratic Formula Standard Form for quadratics is: ax2 + bx+ c Quadratic Formula x = b p b2 4ac 2a A general rule for plugging in the a;b;c in the quadratic formula is to put parenthesis around each value when you plug it in This will help to keep the signs straight 1

Quadratic Formula

Derive Quadratic Formulap 356 Pull Pull 8 p 361 2 7, 18 20 Divide by a Subtract S Complete the square Factor x Algebra 2a 2a x b2 — 4ac

64 The Quadratic Formula

Example 2 Use the Quadratic Formula to Sketch a Parabola Find the x-intercepts, the vertex, and the equation of the axis of symmetry of the quadratic relation y 5 x2 8 3 Sketch the parabola Solution To find the x-intercepts, let y 0 and use the quadratic formula to solve the quadratic equation For x5 2 8x 3 0, a 5, b 8, and c 3 x Therefore

Solve each equation with the quadratic formula

Using the Quadratic Formula Date_____ Period____ Solve each equation with the quadratic formula 1) m2 − 5m − 14 = 0 2) b2 − 4b + 4 = 0 3) 2m2 + 2m − 12 = 0 4) 2x2 − 3x − 5 = 0 5) x2 + 4x + 3 = 0 6) 2x2 + 3x − 20 = 0 7) 4b2 + 8b + 7 = 4 8) 2m2 − 7m − 13 = −10-1-

103 Quadratic Equations and Rotations

is called a quadratic curve If all coeﬃcients vanish, then Q = R2, the full plane If all coeﬃcients vanish except F, then Q = ∅, the empty set If A = B = C = 0 and D2 + E2 > 0, then Q, is a straight line In these cases the terminology quadratic curve is inappropriate The truly quadratic curves are obtained when A2+B2+C2 > 0,