GCSE: Curved Graphs Dr J Frost Last modified: 31 st December 2014 GCSE Revision Pack Reference: 94, 95, 96, 97, 98.

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GCSE: Curved Graphs Dr J Frost Last modified: 31 st December 2014 GCSE Revision Pack Reference: 94, 95, 96, 97, 98

GCSE Specification The diagram shows the graph of y = x 2 – 5x – 3 (a) Use the graph to find estimates for the solutions of (i) x 2 – 5x – 3 = 0 (ii) x 2 – 5x – 3 =

Skill #1: Recognising Graphs Linear The line is known as a straight line. ?? ?

Quadratic The line for a quadratic equation is known as a parabola. ?? ? Skill #1: Recognising Graphs

Cubic x y x y ? ? ? ? Skill #1: Recognising Graphs

Reciprocal ? The lines x = 0 and y = 0 are called asymptotes.  An asymptote is a straight line which the curve approaches at infinity. ? ? You don’t need to know this until A Level. Skill #1: Recognising Graphs

Exponential x y ? Skill #1: Recognising Graphs ?

The equation of this circle is: x 2 + y 2 = 25 ? Circle Skill #1: Recognising Graphs

Quickfire Circles 1 1 x 2 + y 2 = x 2 + y 2 = x 2 + y 2 = x 2 + y 2 = x 2 + y 2 = x 2 + y 2 = 36 ? ? ? ? ? ?

Card Sort Match the graphs with the equations. ABCD EFGH IJKL x) y = x 2 + x - 2 ix) y = 2x 3 i) y = 5 - 2x 2 vii) y=-2x 3 + x 2 + 6x iv) y = 3/x iii) y = -3x 3 viii) y = -2/xii) y = 4 x xii) y = 2x – 3 v) y = x 3 – 7x + 6 xi) y = sin (x) vi) A: quadratic B: cubic C: quadratic D: cubic E: cubic F: reciprocal G: cubic H: reciprocal I: exponential J: linear K: sinusoidal L: fictional Equation types: ? ? ? ? ? ? ? ? ? ? ? ?  Click to reveal answers.

????? Click to brosketch Skill #2: Plotting and recognising trig functions.

Test Your Understanding ? ?

????? Click to brosketch

Quickfire Coordinates ???? ????

SKILL #3: Using graphs to estimate values Bro Tip for (b): Look at what value has been substituted into the equation in each case. ? ? ?

Test Your Understanding ? ?

Using a Trig Graph Q ? Q ?

Test Your Understanding ? ?

Exercise 1 (on provided sheet) Identify the coordinates of the indicated points. 1 1 ? ? ? ? ? 2 a b c ? Match the graphs to their equations. ? 3

Reveal ???? Exercise 1 (on provided sheet) 4

Exercise 1 7 ? ? b c a 5 6 ? ? ? ? ? ? ?

8 ? ? ?

(1,7) (3,175) ? Bro Hint: Substitute the values of the coordinates in to form two equations. You’re used to solving simultaneous equations by elimination – either adding or subtracting. Is there another arithmetic operation?

Test Your Understanding Q  ? ?

Exercise 1 (continued) ? ? ? ?