Mathematics Functions
Parabola
y = ax 2 + bx + c
y = a (x − p) + q
2
Turning points (p;q)
−b
x=
When Sketching: 2a
What is the shape of the graph ?
Find the turning point (also the line of symmetry) Completing the square
Find the y-intercept by making x = 0 y = 2x 2 − 4x − 16
y = 2 (x 2 − 2x − 8)
Find the x-intercept, by making y = 0 2 (x 2 − 2x + 1 − 1 − 8)
Sketch y = 2 (x − 1)2 − 18
t . p . = (1; − 18)
Finding the equation
When given both x-intercepts:
y = a (x − x1) (x − x2)
X-ints that were given
Then sub in any other points that were given to find a
Reflections:
Over the x-axis, negate the y: y = f (x) y = − f (x)
Over the y-axis; negate the x: y = f (x) y = f (−x)
Parabola
y = ax 2 + bx + c
y = a (x − p) + q
2
Turning points (p;q)
−b
x=
When Sketching: 2a
What is the shape of the graph ?
Find the turning point (also the line of symmetry) Completing the square
Find the y-intercept by making x = 0 y = 2x 2 − 4x − 16
y = 2 (x 2 − 2x − 8)
Find the x-intercept, by making y = 0 2 (x 2 − 2x + 1 − 1 − 8)
Sketch y = 2 (x − 1)2 − 18
t . p . = (1; − 18)
Finding the equation
When given both x-intercepts:
y = a (x − x1) (x − x2)
X-ints that were given
Then sub in any other points that were given to find a
Reflections:
Over the x-axis, negate the y: y = f (x) y = − f (x)
Over the y-axis; negate the x: y = f (x) y = f (−x)
