Vocabulary
What is the u-shaped graph shown by a quadratic?
Parabola
Dakota translates the quadratic parent function x2, 10 units to the right and 4 units down. What is the equation of Dakota's function?
y = (x-10)2 - 4
y = x2 - 5
Translated down 5 units
Where is the axis of symmetry located?
The axis of symmetry is located in the middle of the parabola, going through the vertex where it divides a parabola into two symmetric parts
What is the vertex of f(x)=x2
(0,0)
The lowest or highest point on a parabola.
Vertex
Gloria transforms the quadratic parent function x2 by vertically stretching the parabola by a factor of 2. Then, she translates the parabola 8 units up and 6 units right. What is the equation of Gloria's parabola?
y = 2(x-6)2 + 8
y = (x+5)2
Translated to the left 5 units
What is the “ABC” formula for axis of symmetry?
x=-b/2a
What is the vertex of f(x)= -2(x+7)2
(-7,0)
These are THREE names for the place or places a parabola crosses the x-axis.
x-intercept, roots, and zeroes
Makayla begins with the quadratic parent function x2. She reflects the parabola over the x-axis and translates the function 3 units to the left and 5 units down. What is Makayla's equation?
y = -(x+3)2 - 5
y = -x2
Reflected over the x-axis
What is the “Roots” formula for axis of symmetry?
x= r1+r2/2
What is the vertex of f(x) = 9(x + 5)2 - 10
(-5,-10)
What is a word for highest point and what is a word for lowest point?
Maximum and Minimum
Danny transforms the quadratic function x2 by stretching it vertically by a factor of 4 and translating the parabola 22 units down and 1 unit to the left. What is the equation of the transformed function?
y = 4(x+1)2 - 22
Y= (x-7)2+9
Translated up 9 units and to the right 7 units
What is the axis of symmetry of
y = 2x² + 8x – 3?
x=-2
What is the vertex of f(x) = -10(x)2 - 4
(0,-4)
This is the standard form of a quadratic equation.
y= ax2+bx+c
Liz is translating the quadratic parent function x2. She reflects the parabola over the x-axis and vertically compresses by ½. She then translates it 7 units down and 14 units to the left. What is the equation of Liz’s parabola?
Y= -1/2(x+14)2-7
Y= -2(x+2)2-10
Vertically stretched by 2
Reflected over x-axis
Translated down 10 units
Translated to the left 2 units
What is the axis of symmetry of
y = (x +10)(x -6)
x=-2
What is the vertex of f(x)=100(x+89)2-200
(-89,-200)