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Describe the transformations
f(x)=-4(x-1)^2
Reflection across the x-axis, vertical stretch by a factor of 4, horizontal shift to the right by 1 unit
Find the zeros:
h(x)=4x^2+16x
x=0,-4
What is the y-intercept of the function?
h(x)=(x+1)^2-3
(0,-2)
Solve for the zeros by completing the square:
2x^2-8x=22
2+-sqrt(15)
Find the roots by factoring:
4x^2=81
(2x-9)(2x+9)
Use the description to write the quadratic function in vertex form.
f(x)=x^2 is vertically compressed by a factor of 9 and translated 2 units down and 3 units to the left.
g(x)=1/9(x+3)^2-2
CTS to find the zeros of the function:
3x^2+6x=1
-1+-(2sqrt(3))/3
Factor only
9x^2-12x+4
(3x-2)^2
Identify the vertex of the function
f(x)=-1/100000(x+4)^2-5
(-4,-5)
The path of a soccer ball is modeled by the function below where h is the height in meters and x is the horizontal distance that the ball travels in meters. What is the maximum height that the ball reaches?
h(x)=-0.005x^2+0.25x
3.125 m
Factor and solve for the zeros
9k^2+66k+21=0
3(3k+1)(k+7)
k=-1/3 , -7
Write the function in vertex form
h(x)=5x^2-20x+9
h(x)=5(x-2)^2-11
Matthew throws a ball into the air. The ball is thrown from his arms at about 4 feet. The trajectory of the ball's height can be modeled by a quadratic function where h(t) describes the height and t describes the time in the air. The ball reaches its highest point in the air 20 feet above the ground 1 second after it was thrown. What is the initial vertical velocity the ball was thrown in the air with?
32 feet per second
Solve by factoring:
x^2-3/4x+1/8=0
x=1/4,1/2