Verbal Transformations
Dylan sketches a parabola with a vertex at the origin that opens downward. What is the equation of Dylan's function?
y = -x^2
Describe the transformation.
y = (x+1)2 - 5
Translated 1 unit left and 5 units down.
A parabola has a vertex of (2,-11). What is the equation of the axis of symmetry?
x = 2
Determine whether this function has a maximum or minimum value, and find that value:
f(x) = -2(x-1)2+3
max = 3
Given the vertex of (-2, 5) and a point (0, 1), what is the quadratic equation in vertex form?
y = -( x +2 )2 + 5
Marneli translates the quadratic parent function 10 units to the right and 4 units down. What is the equation of Marneli's function?
y = (x-10)^2 - 4
Describe the transformation.
y = 1/6(x-3)2 + 1
Vertically compressed, and translated 3 units to the right and 1 unit down.
A quadratic equation of y= -8x2 -32x+9. What is the equation of the axis of symmetry?
x = -1
Determine whether this function has a maximum or minimum value, and find that value:
f(x) =3(x+2)2-7
Given the vertex of (-3, -4) and a point (1, -6), what is the quadratic equation in vertex form?
y = -1/8(x + 3)2 - 4
Brianna transforms the quadratic parent function 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 Brianna's parabola?
y = 2(x-6)^2 + 8
Describe the transformation.
y = -4(x+2)2 + 4
Reflected across the x-axis, vertically stretched, and translated 2 units to the left and 4 units up.
What can you say about the graph of the parabola when a<0 and when a>0?
When a<0 , it opens downward.
When a>0, it opens upward.
Determine whether this function has a maximum or minimum value, and find that value:
f(x) = -4(x+3)2 +6
max = 6
Given the vertex of (6, -16) and a point (3, 2), what is the quadratic equation in vertex form?
y = 2(x - 6)2 - 16
Nyomi begins with the quadratic parent function. She reflects the parabola over the x-axis and translates the function 3 units to the left and 5 units down. What is Nyomi's equation?
y = -(x+3)^2 - 5
Describe the transformation.
y = -1/3(x)2
Vertically compressed and reflected across the x-axis.
What is the y-intercept of y=-2(x+3)2 +14
(0, -4)
Determine whether this function has a maximum or minimum value, and find that value: f(x) = x2 + 12x + 27
min = -9
Change y = (x - 7)2 - 25 to standard form.
y = x2 - 14x + 24
Stacey transforms a quadratic function 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 Stacey's transformed function?
y = 4(x+1)^2 - 22
Describe the transformation.
y = (2x)2 + 15
Vertical stretch by a factor of 2 and translated 15 units up.
What is the y-intercept of y =1/3( x-9)2 - 7?
(0, 20)
Determine whether this function has a maximum or minimum value, and find that value:
f(x) = -2x2 - 8x +5
max = 13
Change y = -4(x + 5)2 + 61 to standard form.
y = x2 - 40x - 39