Parent Functions and Transformations
Describe the transformation from the parent function.
f(x)=-(x-5)^2+4
Reflection in the x-axis
Horizontal translation 5 units right
Vertical translation 4 units up.
{(x,+,4y,-,2z,=,3),(x,+,3y,+,7z,=,1),(2x,+,9y,-,13z,=,2):}
No Solution
Find the axis of symmetry, the vertex, the minimum or maximum value, and the domain and range of the quadratic function
f(x)=-4(x-2)^2+5
Axis: x = 2 Vertex: (2, 5)
Max of 5.
Domain: All real numbers.
Range: y< 5
A parabola has a vertex of (-3, 5) and contains the point (5, 9). What is the equation of the parabola in vertex form?
f(x)=1/16(x+3)^2+5
Describe the transformation from the parent function.
|1/2x|-7
Horizontal Stretch by 2
Vertical translation 7 units down.
{(5x,-,3y,+,z,=,8),(x,+,2y,-,3z,=,2),(2x,+,4y,-,6z,=,4):}
Infinite Solutions
Find the axis of symmetry, the vertex, the minimum or maximum value, and the domain and range of the quadratic function
g(x) = 5x^2+10x-3
Axis: x = -1 Vertex: (-1, -8)
Min of -8.
Domain: All real numbers.
Range: y> -8
Write the equation of the parabola in intercept form that passes through the point (4, 3) and has the x-intercepts of -1 and 5.
f(x)=-3/5(x+1)(x-5)
Let the graph of g be a translation 2 units up and 4 units right followed by a vertical compression by 1/2 of the graph of
f(x)=x^2
1/2(x-4)^2+1
Solve the system.
{(x,+,y,-,z,=,3),(x,+,3y,+,z,=,3),(2x,+,9y,+,z,=,2):}
(5, -1, 1)
Find the y-intercept of each quadratic function.
f(x) = x^2-5x+7,
g(x)=2(x-1)^2+3
f(0)=7
g(0)=5
A parabola has a vertex of (-1, -2) and contains the point (0, 1). What is the equation of the parabola in standard form?
f(x)=3x^2+6x+1
Let the graph of g be a translation 6 units left and 1 unit down followed by a horizontal stretch by 4 of the graph of
f(x)=x^2
g(x)=(1/4x+6)^2-1
{(x,-,y,+,z,=,-3),(2x,-,y,+,5z,=,4),(4x,+,2y,-,z,=,2):}
(-1, 4, 2)
Describe where the function is increasing and decreasing.
f(x)=-x^2+5
Increasing: x < 0
Decreasing: x > 0
Write the equation of the parabola in standard form that passes through the point (1, -16) and has the x-intercepts of -3 and 2.
f(x)=4x^2+4x-24
Let the graph of g be a vertical stretch by 3 followed by a reflection in the y-axis and then a translation 7 units down of the graph of
f(x)=(x-5)^2+1
g(x)=3(-x-5)^2-4
{(2x,-,5y,-,z,=,17),(x,+,y,+,3z,=,19),(-4x,+,6y,+,z,=,-20):}
(-4/3,-17/3, 26/3)
A passenger on a stranded lifeboat shoots a distress flare into the air. The height (in feet) of the first flare above the water is given by f(t) = -16t(t - 8), where t is time (in seconds) since the flare was shot. The passenger shoots a second flare, whose path contains the vertex (3.5, 196) and has the intercepts (0, 0) and (7, 0). Which flare travels higher? Which remains in the air longer?
The first flare travels higher and is in the air longer.
Write an equation of the parabola that passes through the points (-2, 7), (1, 10), and (2, 27)
y=4x^2+5x+1