What's it Called?
This gives the vertical stretch factor in the vertex form, f(x) = a(x-h)^2 + k, of a quadratic function.
What is "a"?
This quadratic function has been shifted to the left 5 units and down ten units.
What is (x+5)^2-10
y = (x+1)^2 - 5
translated 1 unit left and 5 units down
y = 3x^2 - 6
becomes more narrow by a factor of 3 and translated 6 units down
Zack sketches a parabola with a vertex at the origin that opens downward. What is the equation of Zack's function?
what is y = -x^2
This gives the vertical shift in the vertex form, f(x) = a(x-h)^2 + k, of a quadratic function.
What is "k"?
This quadratic function has been reflected over the x-axis, then moved up three units.
What is -x^2+3
y = 1/6(x-3)^2 + 1
becomes wider by a factor of 1/6, translated 3 units to the right and 1 unit down
y = (2x)^2 + 10
becomes more narrow by a factor of 4 and translated 10 units up
Dakota translates the quadratic parent function 10 units to the right and 4 units down. What is the equation of Dakota's function?
What is y = (x-10)^2 - 4
This gives the horizontal shift in the vertex form, f(x) = a(x-h)^2 + k, of a quadratic function.
What is "h"?
This quadratic function has been stretched by 1/2, shifted three units to the left and down two units.
What is 1/2(x+3)^2-2
y = -4(x+2)^2 + 4
reflected across the x-axis, becomes more narrow, translated 2 units to the left and 4 units up
y = (6x+1)^2 + 9
becomes more narrow by a factor of 36, translated 1 unit left and 9 units up
Gloria transforms the quadratic parent function by narrowing 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
This equation form helps us find the x-intercepts most efficiently.
What is factored form?
This quadratic function has been compressed by 1/4, and shifted up four units.
What is 1/4x^2+4
y = -1/3(x)^2
becomes wider and reflected across the x-axis
y = 5x^2
becomes more narrow by a factor of 5
Makayla 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 Makayla's equation?
y = -(x+3)^2 - 5
This equation helps us find the y-intercept most efficiently.
What is the standard form?
This quadratic function has been compressed by 5, shifted two units to the right and up six.
What is 5(x-2)^2+6
y = (2x)^2 + 15
becomes more narrow by a factor of 4 and translated 15 units up
y = 2/5x^2
becomes wider by a factor of 2/5
Jayden transforms a quadratic function by narrowing it by a factor of 4, translating it 22 units down and 1 unit to the left. What is the equation of the transformed function?
y = 4(x+1)^2 - 22