Quadratic Functions from Quadratic Patterns

In the year 3000, Avery is playing an advanced AI math puzzle game on Mars. To unlock the next level, Avery needs to solve a quadratic equation embedded in the game's code: x^2 - 5x + 6 = 0. The solution requires factoring. What are the values of x that Avery should input to proceed?

• x = 2, 3

• x = 1, 6

• x = 4, 5

• x = -2, -3

Emma, Olivia, and Kai are space explorers trying to calculate the number of starfruits (x) they will have after they combine their collections from different planets. They found that the relationship between the number of starfruits they have can be represented by the interstellar equation 2x^2 + 5x - 3 = 0. Help them solve this equation using the cosmic quadratic formula.

• 1, -3/2

• 1, -2/3

• 2, -3/2

• 3/2, -1

Lyra is optimizing the pricing algorithm for her interstellar trading bot. If the profit function is modeled by the quadratic equation 3x^2 - 7x + 2 = 0, where x represents the price in galactic credits, what are the two price points that maximize her trading profits?

• -2, -1/3

• 4, -1/3

• 2, -1/3

• 2, 1/3

In the year 3000, Lily is working on a mathematical algorithm for a quantum computer. She needs to write a quadratic function that represents the holographic area of a hypercube, with the length of a side being (x + 5) light years. She comes up with the equation ax^2 + bx + c. In which form is Lily's quadratic function written?

• Standard form

• Factored form

• General form

• Vertex form

In the year 3000, a young scientist named Mia is studying advanced algorithms for programming AI robots. She comes across a mathematical function in the form of a(x - h)^2 + k in the robot's programming code. What is this form called in the field of quadratic functions?

• Factored form

• General form

• Standard form

• Vertex form

In a distant future, Elijah is analyzing the energy output patterns of a new form of hyper-efficient solar panels and encounters the mathematical expression a(x - r)(x - s). Which form of a quadratic function does this represent?

• Standard Form

• Generic Form

• Factored Form

• Vertex Form

In the year 3000, Zorgon is trying to calculate the energy output of his plasma reactor. He models his energy output as a quadratic function y = (x-1)(2x-1), where x is the number of plasma cells used. What is the standard form of this quadratic function?

• 2x^2 - 3x - 1

• 2x^2 - 3x + 1

• 2x^2 + 3x - 1

• 2x^2 + 3x + 1

In a futuristic simulation, Abigail is analyzing the trajectory of a drone flying through the air. The equation representing the altitude of the drone over time is y = x^2 + 4x - 3. What is the vertex form of this quadratic function?

• y = (x - 2)^2 - 7

• y = (x + 2)^2 - 7

• y = (x + 2)^2 + 7

• y = (x - 2)^2 + 7

In the year 3000, Abigail is navigating through a virtual reality game where she must solve the quadratic equation x^2 + 4x + 4 = 0 to unlock the next dimension. Assist Abigail in finding the solution by simulating the equation in a holographic graph.

• -1

• 0

• 2

• -2