Graphs and Functions Revision I Workbook Summary

1. Quadratic Functions - Expanding binomials and using identities - Completing the square to find turning point form - Solving quadratics using factorisation, the quadratic formula, and discriminant - Discriminant determines number of real solutions

2. Graphing Quadratics - Intercept form: y = a(x-b)(x-c) - Turning point form: y = a(x-h)^2 + k - Identify axis of symmetry, turning point, x- and y-intercepts

3. Finding Rules from Graphs - Use intercept or turning point form depending on visible features - Substitute another point to solve for a

4. Quadratic Inequalities - Solve equation, sketch graph, use graph to find solution regions

5. Hidden Quadratics - Substitute complicated expressions with a variable - Solve like a normal quadratic then reverse the substitution

6. Rectangular Hyperbolas - Form: y = a / (x - h) + k - Vertical asymptote x = h, horizontal asymptote y = k - Reflect if a is negative

7. Truncus - Form: y = a / (x - h)^2 + k - Similar asymptotes as hyperbola - Reflect if a is negative

8. Square Root Functions - Form: y = añ(x - h) + k - Endpoint at (h, k) - Reflections based on sign of a and inside root

9. Rational Power Functions - Form: y = A(x - h)^(n/m) + k - Number of branches and shape depend on whether m is even or odd - Range and steepness depend on n and m

10. Circles - General form: (x - h)^2 + (y - k)^2 = r^2 - Expanded form: x^2 + y^2 - 2hx - 2ky + c = 0 - Complete the square to convert between forms

11. Semicircles - Rearranged from circle equations - For y: y = ±√(r^2 - (x - h)^2) + k - For x: x = ±√(r^2 - (y - k)^2) + h