A3 & A4 Quadratics

Question 1

What are the four steps to sketching a quadratic graph?

Answer 1

Use the equation y = ax2 + bx + c

1. Is the curve positive or negative?

curve = positive if a = positive

curve = negative if a = negative

2. y intercept:

y intercept = c

3. x intercept(s):

Factorise the equation ax2 + bx + c using salt and pepper if a is bigger than 1.

4. Find the turning point:

Complete the square on ax2 + bx + c to find turning points of x and y and put these values into coordinates for the turning point.

Question 2

How would you solve a quadratic by factorising when x2 (squared) is bigger than 2?

Answer 2

E.g. x3 + 5x2 + 6x = 0

Factorise all of it to get an equation starting with x2 on its own (taking out a common factor):

x (x2 + 5x + 6) = 0

Factorise the middle (part in brackets):

x (x+2) (x+3) = 0

So x = 0, or x = -2, or x = -3.