Quadratic Equations
Solve (x-2)(x+3)=0
x=2, x=-3
How is the parent graph y=x2 transformed by the equation y=(x+3)2?
Translation left by 3 units
What is the domain of the function y=x2 ?
x is any real number
Is f(x) = |x| odd, even or neither?
Even
Where is the centre of the circle (x-2)2+(y+5)2=4?
(2, -5)
Solve (2x-3)(3x+4)=0
x=-4/3, x=3/2
How is the parent graph y=x2 transformed by the equation y=2x2-1?
Vertical stretch of factor 2; translation down by 1 unit
What is the domain of the function f(x)=1/x ?
x is any real number except 0
Is f(x) = 1/x odd,even or neither?
Odd
What is the radius of the circle (x-6)2 +y2-1=0?
1 unit
Solve x2-2x-35=0
x=-5, x=7
How is the parent graph y=3x transformed by the equation y=3x-7-2 ?
Translation of 7 units to the right; translation of 2 units down
What is the range of the function y=|x| ?
y is any real number greater than or equal to 0
Is f(x) = 1/(x-2) odd, even or neither?
Neither
What are the centre and radius of the circle x2+(y+3.5)2-121=0?
(0, -3.5); 11 units
Solve 2x2-3x+1=0
x=0.5, x=1
What equation would translate the parent graph y=|x| 1 unit to the right, stretch it vertically by a factor of 2, & reflect it in the x-axis?
y = -2|x-1|
What is the range of the function y=(x-1)2-6?
y is any number greater than or equal to -6
How can you tell that a function is even from its graph?
The graph has line (reflective) symmetry in the y-axis
Where is the centre of the circle (x2+4x+4)+(y2-6y+9)=25?
(-2, 3)
Solve 3x2+5x=2
x=1/3, x=-2
What are the equations of the asymptotes of the function
f(x) = 8 + 1/(x+4) ?
x=-4; y=8
What are the domain and range of the function y=|x-5|+2?
Domain: x is any real number
Range: y is any number greater than of equal to 2
What is special about the graph of an odd function?
It has rotation symmetry of 180 degrees about the origin
Where is the centre of the circle x2-8x +y2+2y-19=0?
(4, -1)