Name that Transformation
Compare the graph to its parent function.
f(x)=1/2x^2-7
Vertical Compression by 1/2
Vertical translation 7 units down
Find the axis of symmetry and the vertex of the parabola.
f(x)=-5(x+8)^2-11
AoS: x = -8
V(-8, -11)
Write a quadratic function whose graph satisfies the given condition(s).
Vertex: (-7, 4)
f(x)=(x+7)^2+4
Write in standard form.
f(x)=-4(x+5)(x-2)
f(x)=-4x^2-12x+40
Find the x-intercepts of the parabola.
f(x)=x^2-7x+6
x = 6 and x = 1
Compare the graph to its parent function.
g(x)=-(x+5)^2+9
Reflection over the x-axis
Horizontal translation 5 units left
Vertical translation 9 units up
Find the axis of symmetry and the vertex of the parabola.
f(x)=5(x-7)(x+3)
AoS: x = 2
V(2, -125)
Write a quadratic function that has taken the parent function and vertically stretched it by a factor of 5, then translated it 7 units right and 3 units up.
g(x)=5(x-7)^2+3
Write in standard form.
f(x)=-(x+4)^2+8
f(x)=-x^2-8x-8
Find the x-intercepts of the parabola.
f(x)=x^2-3x-10
x = 5 and x = -2
Using the transformation from the graph of f to the graph of g, write the new equation.
{(f(x)=-(x+1)^2-2),(g(x)=f(x)+9):}
g(x)=-(x+1)^2+7
Find the axis of symmetry, the vertex, and the y-intercept of the parabola.
g(x)=-2x^2-12x+9
AoS: x = -3
V(-3, 27)
y-int: 9 or (0, 9)
Write a quadratic function in vertex form whose graph has the given vertex and passes through the given point.
Vertex: (1, 2); passes through (2, -5)
f(x)=-7(x-1)^2+2
Write in factored form.
f(x)=6x^2+33x+15
f(x)=3(2x+1)(x+5)
Find the x-intercepts of the parabola.
f(x)=-5x^2+45
x = -3 and x = 3
Describe the transformation from f(x) to g(x).
{(f(x)=-(x+1)^2-2),(g(x)=-4(x-5)^2+8):}
Vertical Stretch by 4
Right 6
Up 10
Find the y-intercept.
f(x)=-2(x-4)^2+7
-25 or (0, -25)
Write a quadratic function whose graph satisfies the given conditions.
passes through (-5, 0) (-1, 0) and (3, 16)
g(x)=1/2(x+5)(x+1)
Write in vertex form.
f(x)=x^2+10x-7
f(x)=(x+5)^2-32
Find the x-intercepts of the parabola.
f(x)=15x^2+7x-2
x = 1/5 and x = -2/3
Write a function that transforms the parent function with a horizontal transformation 3 units right and a vertical transformation 6 units up followed by a vertical compression by 1/2.
g(x)=1/2(x-3)^2+3
A football is kicked into the air and follows the path
h(t)=-16t^2+48t
Find the maximum height of the football. What is the domain and range?
Max height 36 feet.
Domain 0< x < 3
Range 0 < y < 36
Using the transformation from the graph of f to the graph of g, write the new equation.
{(f(x)=(x+5)^2-4),(g(x)=2f(x-3)):}
g(x)=2(x+2)^2-8
Write in vertex form.
f(x)=5x^2+30x-1
f(x)=5(x+3)^2-46
Find the x-intercepts of the parabola.
f(x)=(x+3)^2-36
x = -9 and x = 3