Different types of Quadratic graph and how to interpret them Quadratic Equations Different types of Quadratic graph and how to interpret them

Quadratic Equations y = x2 y = x2 + 3 y = 6x2 y = -x2 -4 -3 -2 -1 0 1 2 3 4 y = x2 + 3 + 3 moves the curve up the y axis by 3 – the same effect as with linear equations y = 6x2 y = -x2 6x2 – the coefficient of x2 makes the parabola narrower If the coefficient was less than 1, for example 1 2 then the parabola would be wider -x2 – a negative coefficient of x2 turns the parabola upside down

Find the solutions for 2x2 - 4=0 Quadratic Equations Finding solutions Find the solutions for 2x2 - 4=0 If we think about the equation: y = 2x2-4 We are looking for the values of x such that y = 0 y = 0 i.e. 0 = 2x2 - 4 or 2x2 – 4 = 0 because equals means ‘is the same’ we can write it either way is also the equation for the horizontal line through the origin of the axes

Plot the line y = 2x2 - 4 and the line y = 0 on a graph Quadratic Equations Plot the line y = 2x2 - 4 and the line y = 0 on a graph The coordinates where the lines cross are (-1.4,0) and (1.4,0) 50 45 40 35 30 25 20 15 10 5 -5 -10 So when y = 0 x = -1.4 and x = 1.4 y = 2x2 - 4 These are the solutions to: 2x2 - 4=0 There are usually 2 solutions to quadratic equations because of the shape of the graph y = 0 -4 - 3 - 2 - 1 0 1 2 3 4

This can be repeated to find the solution of 2x2 - 4 = 10 Quadratic Equations This can be repeated to find the solution of 2x2 - 4 = 10 50 45 40 35 30 25 20 15 10 5 -5 -10 Draw the lines y = 2x2 - 4 and y = 10 The coordinates where the lines cross are approximately (-2.6,10) and (2.6,10) y = 2x2 - 4 So when y = 10 x = -2.6 and x = 2.6 y = 10 -4 - 3 - 2 - 1 0 1 2 3 4

Quadratic Equations Match the letter of the graph with the number Worksheet 1 Answers Quadratic Equations Match the letter of the graph with the number of the equation C B D C A D 1. y = x2 2. y = x2 + 5 B 3. y = 4x2 + 7 4. y = -x2 - 5 A

AQA Module 5 Foundation p263 Answer Sheet Worksheet 2 - Answers Quadratic Equations AQA Module 5 Foundation p263 Answer Sheet y = x2 + 2x + 1 x -4 -3 -2 -1 1 2 y 9 4 y = x2 - 4x x -1 1 2 3 4 5 y -3 -4 1. 2.

AQA Module 5 Foundation p263 Answer Sheet Worksheet 3 - Answers Quadratic Equations AQA Module 5 Foundation p263 Answer Sheet y = x2 - 3x x -1 1 2 3 4 5 y -2 10 y = 5 + x - x2 x -3 -2 -1 0.5 1 2 3 4 y -7 5 5.25 3. 4.

Quadratic Equations Match the letter of the graph with the number Worksheet 1 Quadratic Equations Match the letter of the graph with the number of the equation C -4 -3 -2 -1 0 1 2 3 4 D 1. y = x2 2. y = x2 + 5 B 3. y = 4x2 4. y = -x2 - 3 A

AQA Module 5 Foundation p263 Answer Sheet Worksheet 2 Quadratic Equations AQA Module 5 Foundation p263 Answer Sheet y = x2 + 2x + 1 x -4 -3 -2 -1 1 2 y 9   4 y = x2 - 4x x -1 1 2 3 4 5 y   -4 -3 1. 2.

AQA Module 5 Foundation p263 Answer Sheet Worksheet 3 Quadratic Equations AQA Module 5 Foundation p263 Answer Sheet y = x2 - 3x x -1 1 2 3 4 5 y   -2 y = 5 + x - x2 x -3 -2 -1 0.5 1 2 3 4 y -7   5.25 3. 4.