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Rewrite the function f(x) = x2 + 6x + 20 in vertex form. (Don't forget to write "f(x) ="!)
What is the coordinate of the vertex of the function f(x) = x2 + 6x + 20?
Rewrite the function g(x) = x2 - 24x - 6 in vertex form. (Don't forget to write "g(x) ="!)
Match each equation on the left with the equivalent equation on the right. (Note: one of the equations on the right will not be used.)
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
| arrow_right_alt | x2 - 2x = 11 | |
(x + 4)2 = 16 | arrow_right_alt | (x + 4)2 = 12 |
x2 - 2x + 1 = 0 | arrow_right_alt | x2 + 8x = 0 |
(x - 1)2 = 12 | arrow_right_alt | (x - 1)2 = 0 |
x2 + 8x = -4 | arrow_right_alt | x2 - 2x = 10 |
(x - 1)2 = 11 | arrow_right_alt | (x + 4)2 = 18 |
x2 + 8x = 2 | arrow_right_alt | (x + 4)2 = -4 |
Solve the equation x2 + 14x = - 24 by completing the square.
Solve the equation x2 + 14x = - 24 with The Quadratic Formula.
What is one solution to the equation x2 + 14x = -24?
What is the other solution to the equation x2 + 14x = -24?
What is the value of a for the given application of The Quadratic Formula?
What is the value of b for the given application of The Quadratic Formula?
What is the value of c for the given application of The Quadratic Formula?
Write an equation below that could be solve by this application of The Quadratic Formula?
Fill in the blank to make the expression a complete square: a2 + 18a + ____.
Fill in the blank to make the expression a complete square: (3b + 5)( ____ + 5).
Fill in the blank to make the expression a complete square: c2 - ____c + 64.
Fill in the blank to make the expression a complete square: 9x2 + 12x + ____.
Fill in the blank to make the expression a complete square: (6e - ____ )(6e - 11).
Fill in the blank to make the expression a complete square: f2 - 10f + ____.
Fill in the blank space to solve the equation 2x2 - 3x + 3 = 17 with The Quadratic Formula.
Fill in the blank space to solve the equation 2x2 - 3x + 3 = 17 with The Quadratic Formula.
Fill in the blank space to solve the equation 2x2 - 3x + 3 = 17 with The Quadratic Formula.
Fill in the blank space to solve the equation 2x2 - 3x + 3 = 17 with The Quadratic Formula.
Fill in the blank space to solve the equation 2x2 - 3x + 3 = 17 with The Quadratic Formula.
What is one solution to the equation 2x2 - 3x + 3 = 17?
What is the other solution to the equation 2x2 - 3x + 3 = 17?
What is the exact solution to the equation a2 + 4a = 7 using
notation?
What is one approximate solution to the equation a2 + 4a = 7? (round to the nearest hundredth.)
What is the other approximate solution to the equation a2 + 4a = 7? (round to the nearest hundredth.)
What is the exact solution to the equation b2 - b - 3.5 = 0 using
notation?
What is one approximate solution to the equation b2 - b - 3.5 = 0? (round to the nearest hundredth.)
What is the other approximate solution to the equation b2 - b - 3.5 = 0? (round to the nearest hundredth.)
What is the exact solution to the equation 3c2 + 11c + 4 = -3 using
notation?
What is one approximate solution to the equation 3c2 + 11c + 4 = -3? (round to the nearest hundredth.)
What is the other approximate solution to the equation 3c2 + 11c + 4 = -3? (round to the nearest hundredth.)
The function h(t) = -16t2 + 192t + 30 models the height of an object, in feet, t seconds after it was launched. How fast (in ft./sec.) is the object traveling at the moment it is launched?
The function h(t) = -16t2 + 192t + 30 models the height of an object, in feet, t seconds after it was launched. What is the object's height (in feet) at the moment it is launched?
The function h(t) = -16t2 + 192t + 30 models the height of an object, in feet, t seconds after it was launched. The object hits 350 feet twice. Write an equation that could be solved to find how long it takes for the object to be 350 feet above the ground.
Solve your equation. What is one time that the object is at exactly 350 feet above ground?
What is the other time that the object is at exactly 350 feet above ground?
How long (in seconds) does it take for the object to reach its maximum height?
What is the maximum height of the object?
What is the coordinate of the vertex of the function g(x) = x2 - 24x - 6?
Rewrite the function h(x) = x2 + 5x + 11 in vertex form. (Don't forget to write "h(x) ="!)
What is the coordinate of the vertex of the function h(x) = x2 + 5x + 11?