Vocabulary
Every quadratic equation has a U-shaped graph called this.
What is parabola?
The axis of symmetry for the quadratic y = x^2 + 2x + 1.
What is x = -1?
The axis of symmetry for the quadratic y = (x - 3)^2.
What is x = 3?
The transformations that occur to the function f(x) = x^2 with the quadratic g(x) = (x - 4)^2 - 7.
What are right 4 and down 7?
When a frisbee is thrown up in the air, the equation of its pathway can be modeled by h = -16t^2 + 90t + 5. Find how long it takes to reach the maximum height. (Round to the nearest tenth).
2.8 seconds
The highest or lowest point on a parabola.
What is the vertex?
The axis of symmetry for the quadratic y = 2x^2 - 8x + 3.
What is x = 2?
The axis of symmetry for the quadratic y = (x + 2)^2 - 1.
What is x = -2?
The transformations that occur to the function f(x) = x^2 with the quadratic g(x) = -x^2 + 2.
What are reflected over the x-axis and up 2?
When a frisbee is thrown up in the air, the equation of its pathway can be modeled by h = -16t^2 + 90t + 5. Find the maximum height. (Round to the nearest tenth).
131.6 feet
When a quadratic equation is written in this form y = ax^2 +bx + c
What is the standard form?
The vertex of the quadratic y = x^2 - 4x + 8.
What is (2, 4)?
The vertex of the quadratic y = (x - 3)^2 + 4.
What is (3, 4)?
The transformations that occur to the function f(x) = x^2 with the quadratic g(x) = 2(x + 1)^2 + 3.
What are a stretch, left 1, and up 3?
The function h(t)= -16t^2 + 16t models the height, in feet, of a cat t seconds after it jumps. What is the maximum height of the jump?
What is 4 feet?
The line that runs through the vertex and divides the parabola in half.
What is axis of symmetry?
The vertex of the quadratic y = 2x^2 - 1.
What is (0, -1)?
The vertex of the quadratic y = -x^2 + 3.
What is (0, 3)?
The equation of the new function in vertex form after the transformations of a reflection over the x-axis, then translated 2 units right and 2 units up.
What is y = -(x - 2)^2 + 2?
When Molly jumps off a diving board, the equation of her pathway can be modeled by h = -16t^2 + 13t + 10. Find Molly’s maximum height. (round to the nearest tenth)
12.6 feet
The equation h(t) = -16t^2 + vt + h where h represents the height of an object, in feet, t seconds after it is launched into the air.
What is the vertical motion model?
The vertex of the quadratic y = -3x^2 - 12x + 1.
What is (-2, 13)?
The vertex of the quadratic y = 2(x + 5)^2 - 3.
What is (-5, -3)?
The equation of the new function in vertex form after the transformations of a compression of 1/2, then translated 3 units left and 6 units down.
What is y = 1/2(x + 3)^2 - 6?
Mrs. Minialga wants to surround a 4 in. by 8 in. painting with a frame that is x inches wide. Write a quadratic function A in standard form to represent the combined area of the painting and frame.
y = 4x^2 + 24x + 32