Quadratics - what you should know

Question 1

How to sketch quadratic curve (parabola)

Answer 1

Find the slope (happy or sad) happy is positive coefficient of the x squared sad is negative
Find roots i.e. y=0
Find x=0
Use symmetry to find turning point.

Question 2

How to find equations from graph

Answer 2

Use x roots on graph and insert them as a in (x-a), then use a point on the graph and insert them as x and y, then solve equation to find k then state equation as before but with k subbed in for its true value.

Question 3

How to find turning points from completing the square.

Answer 3

Find what makes the brackets = 0 will be x value and number outside graph will be y axis.
X axis is also axis of symmetry.

Question 4

Completing the square process

Answer 4

Divide entire equation by coefficient of x squared if it exists, if not continue normally.
When finding what the squared bracket is equal to remember to also times the bracket by the coefficient after squaring.

Question 5

Graph of derivative -

Answer 5

Use stationary points of graph to determine roots of graphs with positive and negative gradients depending on whether that area of the graph is positive or negative