Section 5.6
Write the equation in standard form:
(x + 4)(x - 3)
x2 + x -12
A focus and directrix are the ______ distance from any coordinate on a parabola.
Same
If f(x) = 3 and g(x) = x2 + 3x + 5, where does f(x) = g(x)?
x2 +3x + 2
What is the transformation of :
f(x) + k
Move UP
How many x-intercepts does a quadratic function have?
0,1, or 2
Write the equation in standard form
(x + 2)(x + 4) + 7
x2 +6x + 15
What is the distance formula
√(x2 -x1)+ (y2 -y1)
If f(x) = -4x + 5 and g(x) = 2x2 -7x + 3, where does f(x) = g(x)?
2 and -1/2
What is the transformation of :
f(x-h)
Move right
Where does a quadratic function have symmetry?
At the vertex (or axis of symmetry)
Write the equation in standard form:
(x + 3)(x + 1) = -4
x2 +4x + 7
The following parabola has a focus at (-1,-3) and directrix line at y=4. What is the equation of the line?
-1/14x2 -1/7x + 3/7
If f(x) = -2x-8 and g(x) = 54x2 + 208x -308, where does f(x) = g(x)?
1.1 and -5
Original function: g(x) = 2x2 + 3
Transformation: f(x) = g(x-2) + 4
Write the function in standard form.
2(x - 2)2 + 7
If a graph of a parabola is positive, what is the end behavior?
x -> ∞, y -> ∞
x -> -∞, y -> ∞
Write the equation in standard form:
(x + 4)2
x2 +8x + 16
The following parabola has a focus at (2,5) and directrix line at y=3. What is the equation of the line?
1/4x2 - x + 5
If f(x) = -x2 -3x+12 and g(x) = 2x2 + 6x , where does f(x) = g(x)?
-4 and 1
Original function: g(x) = -1/8(x - 4)2 -2
Transformation: f(x) = g(x+5) -4
Write the function in standard form.
1/8(x +1)2 -6
If the graph of a quadratic function has no solutions, how many x-intercepts does it have?
None
-(x+4)(x-3) +5x
-x2 +4x + 12
The following parabola has a focus at the origin and directrix line at y=7. What is the equation of the line?
-1/14x2 +7/2
If f(x) = -3(x-4)2 +12 and g(x) = (x+2)2 + 3x -13, where does f(x) = g(x)?
(5+i√2 )/ 4 and (5 - i√2)/4
Original function: g(x) = (x + 6)2 -3
Transformation: f(x) = g(x-2) + 4
Write the function in standard form.
(x + 4)2 +1
Where does the graph of a quadratic function have a negative interval?
Below the x-axis