A quadratic function is of the formf(X) = ax-+ bx + c and when we set f(x), or y, equal to zero we call it a quadratic equationax + bx +c = 0. When we set y equal to zero and solve for x we are finding the x- intercepts. Here are three quadratic equations: y = x2- 2x – 1 y = - 3x²+12x – 12 y = x2-6x + 13 Using your graphing calculator find the x-intercepts, y-intercepts, and the maximum or minimum values of the quadratic equations. • Confirm your answers using the Quadratic Formula program. • Last, since your calculator only gives real number approximate answers for the zeroes solve these by hand to provide us with exact answers (might be complex numbers).

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A: It can be expressed as the general form of parabola.

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A: Zeros are points where function vanishes.

Q: Complete the square of the quadratic function f(x) = 3x² - 18x + 26.

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Q: By graphing the quadratic function f(x) = 16+ 12x + 2x², find the - and y-intercepts. x- Oz: 16; y:…

A: Given quadratic equation f( x ) = 16 + 12x + 2x2

Q: Suppose f (x) = x² + 2x + 1. Find the vertex, vertical intercept, and x-intercepts of this quadratic…

A: The objective of the question is evaluate vertex , vertical intercept and  x-intercept.

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A: The graph of the quadratic function y=a(x-h)2+k, where a,b,c are number with a not equal to zero The…

Q: The quadratic equation y = - 0.4(x + 2)(x – 4) is in factored form. What are the x-intrecepts for…

A: We put y=0 and solve for x to get the x-intercepts.

Q: Write a quadratic function that fits the points (2, 27), (4, 61), and (7, 142).

A: According to the given question, y(2) = 27 y(4) = 61 y(7) = 142

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Q: The table gives methane gas emissions in millions of metric tons. The quadratic model y = 0.0429x² -…

A: The given model for the methane gas emission is y=0.0429x2-9.73x+706. We have to find the emissions…

Q: n rewriting the function y = ²-5-20 by completing the square, at which of the following equations…

A: We have to rewrite the given equations in square form.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.