Quadratic Equations Jeopardy Game

Quadratics, The Discriminant, Roots of A Quadratic Equation

Domain, Range, Vertical Line test

Diagnostic Assesment( A quick 3 question quiz that you can use as a pre-assement before playing the game.)

Welcome to a Jeopardy Game based on quadratic equations,discriminant and graphs of parabolas.

Solve Quadratic Equations	The Discriminant	Composition of Functions
100 Solve the quadratic Equation Below y = x2 - 2x - 3 The easiest way to solve this is by factoring: (x – 3)(x + 1) x = 3 and x = -1	100 Look at the picture below. WHich of the following numbers could be the discriminant of either graph A) 0 B) -9 C) 10 III. 10 is the only possible answer since this picture shows a positive discriminant.	100 If f(x) = 2x + 3 and g(x) = x – 1 What is (f * g)(2)? g(2) = 2 – 1 = 1 Now substitue the 1 into f f(1)= 2(1)+ 3 = 5
100 Solve the quadratic Equation Below y = x2 + 2x - 3 Factoring is the easiest method here: (x +3)(x – 1) x = 1 and x = -3	100 Classify the roots of the following equation y = x - 2x + 1 A) Imaginary B) Real and Equal B) Real , Unequal and Irrational B) Real , Unequal and Rational a =1 b = - 2 c = 1 Using our general formula, the discriminant is Disciminant: (-2)2 - 4�1 �1 = 4 - 4 = 0 Since the discriminant is zero, we should expect 1 real solution which you can see pictured in the graph below.	100 If f(x) = 5x + 3 and g(x) = 2x – 1 What is f ( g (3))? g(3) = 2(3) –1 = 5 f(5) = 5(5) +3 = 28
200 Solve the quadratic Equation Below y = 9 – x2 This can be factored as a difference of squares (3 − x)(3 + x) 3 − x = 0 3 = x 3 + x = 0 x = - 3 {3, -3}	200 Classify the roots of the following equation y = x2 + 25 A) Imaginary B) Real and Equal B) Real , Unequal and Irrational B) Real , Unequal and Rational a =1 b = 0 c = 25 the discriminant = b2 - 4(a)(c) = 02 - 4(1)(25) - 100 = - 100 Since the discriminant is negative , there are two imaginary solutions to this quadratic equation. The solutions are 5i and -5i	200 If f(x) = 2x and g(x) = x + 1 What is (f * g)(x) Substitute the entire g(x) in for 'x' in f(x) f((g(x)) = 2(g(x)) = 2(x+1) = 2x + 2
300 Solve the quadratic Equation Below y = 32x2 + 8x Again, this can be factored : 0 = 32x2 + 8x 0 = 8x(4x + 1) 8x = 0 x = 0 4x + 1 = 0 x = - ¼	200 Is the equation below a relation, a function, or a 1 to 1 function? 9x2 + 4y2=36 Relation. This is the equation of an ellipse and doesn't pass the vertical or horizontal line tests .	200 If f(x) = x2 and g(x) = x – 1 What is (g* f)(x) g(f(x)) = (x2) – 1
300 Solve this quadratic Equation y = x2 - 4x + 5 and its solution This quadratic equation has imaginary roots.	300 Is the equation below a relation, a function, or a 1 to 1 function? xy = 11 1 to 1 function this is the one type of hyperbola that is a 1 to 1 function.	300 The accompanying tables define functions f and g What is (g * f)(3)? f(3) = 5 g(5) = 8