New 9-1 Maths GCSE Problem Solving 6 - Algebra and Geometry Question - Grades 5-9

[Problem Solving 6 in the Series ( check out 1-5)]
Students should learn/discover
1 .Solve a quadratic equation by ( factorising, formula or completing the square)
2. Find the coordinates where line crosses the y-axis or x-axis
3. Re-write expression using completing the square and find turning points
4. Expand from completing the square to get an equivalent expression
5. From roots of the quadratic equations find the factors and expand expression.

Then use these skills A-E to do the PROBLEM SOLVING Questions on Algebra
Find the y-intercept , x -intercept and turning points on quadratic graph
Find the equation of the quadratic graph from sketch and factors and find the turning point
Find the equation of the curve from the turning point and find roots.
A. a student sheet has no formulae/knowledge as they have to discover these themselves....(starting from a blank canvass- or prior knowledge)
They may use textbooks, on-line resources , their exercise books etc...
B. A COMBINED sheet which acts as a teacher Guidance/Answer sheets
The teacher's role is of a prompter- the student does all the work....It can be a one-one or paired or group work and can be adapted to do other things...