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12.2 Solve Quadratics by Graphing NAME: Corrective Assignment DATE: Find the roots and vertex of the functions graphed below. 1. 2. 3. 4. Roots: Roots: Roots: Roots: Vertex: Vertex: Vertex: Vertex:

How to fill out 12 2 solve quadratics

How to Fill Out 12 2 Solve Quadratics:

1. Begin by understanding the basics of quadratic equations. Quadratic equations are second-degree polynomial equations in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
2. Consider the given equation 12x^2 + 2x = 0. Here, we have a quadratic equation with a coefficient of 12 for the x^2 term and a coefficient of 2 for the x term.
3. To solve the quadratic equation, we can use factoring, the quadratic formula, or completing the square methods. Each method has its advantages and suitability depending on the given equation.
4. In our case, let's solve the quadratic equation 12x^2 + 2x = 0 using factoring. In this method, we want to factorize the equation into two binomials with the product equal to zero.
5. Factor out the common term, which is 2x in this case, from both terms: 2x(6x + 1) = 0.

Set each factor equal to zero and solve for x:

1. 2x = 0 → x = 0
2. 6x + 1 = 0 → 6x = -1 → x = -1/6

Who Needs 12 2 Solve Quadratics:

Quadratic equations are a fundamental concept in mathematics and have various real-life applications. Different individuals or professionals who may need to solve quadratics include:

1. Students studying mathematics or physics: Quadratic equations are commonly taught in high school or college-level math courses. Understanding how to solve them is crucial for further mathematical concepts and problem-solving.
2. Engineers and scientists: Quadratic equations are prevalent in fields such as mechanical engineering, electrical engineering, physics, and chemistry. These professionals often encounter quadratic equations when analyzing motion, electrical circuits, or chemical reactions.
3. Financial analysts and economists: Quadratic equations can also be applied in finance and economics. For example, they can be used in calculating profit-maximizing solutions or determining the optimal production levels in business decisions.
4. Architects and designers: Quadratic equations are useful for architects and designers when dealing with structural designs or creating curves in architecture or industrial design.
5. Problem solvers and critical thinkers: Even outside of specific professions, being able to solve quadratic equations enhances problem-solving skills and critical thinking abilities. It allows individuals to analyze and approach various complex problems using mathematical concepts.

In conclusion, solving quadratic equations like 12x^2 + 2x = 0 requires understanding the steps involved in factoring. This knowledge is relevant to students, professionals in various fields, and individuals seeking to improve their mathematical and problem-solving skills.

Video instructions and help with filling out and completing 12 2 solve quadratics by graphing

Instructions and Help about 12 2 solve quadratics

In this video we're going to take a look at solving quadratic equations by graphing remember we have several ways to solve quadratic equations including graphing we can also factor we could complete the square, and we could use the quadratic formula and graphing is just another way and as we do that what we're going to do is we're going to go ahead, and we're going to graph the function that is related to the equation that we're trying to solve and by that I mean for this one we're going to graph the equation y equals x squared minus 4x plus 4 and then what we're going to do is we're going to take a look at the graph and look for the place where y is equal to 4 our excuse me y is equal to 0 0 got a random 4 in there y is equal to 0 and where is that well that is located on the x-axis so what we're really going to be looking for when we're solving by graphing is where does the graph contact the x-axis and there are three things that can happen one of those things is that the graph can cross the x-axis something like this and if that's the case we would have two solutions there would be one here and one there another thing that can happen is the graph can just touch the x-axis like that the vertex of it is on the x-axis and in that case we have one solution a final third thing that can happen is the graph will never touch the x-axis something like that and in that case we don't have any real solutions that's where imaginary numbers start to come in, but we're not going to worry about imaginary numbers quite yet alright so first thing we want to do and graph in this well it would be good to know the standard form and remember standard form for a quadratic equation is y equals ax squared plus BX + C okay why am I interested in standard form because the first thing I'm going to want to do here is figure out what the vertex is, and we start by finding it the axis of symmetry and the axis of symmetry remember is negative B over 2a and that's equal to X so let's figure out what the axis of symmetry is we start with the negative be on top in this case B is negative 4, so I'm going to have negative 4 over 2 times a and in this case an is just 1 so 2 times 1 okay negative 4 is going to give me a positive 4 and then on the bottom we've got 2 times 1 which is just going to be to this simplifies to 2 okay that is my axis of symmetry and remember axis of symmetry is a line so x equals 2 is my axis of symmetry now we also know that the vertex of a parabola is on the axis of symmetry so what we could do is take that value that we just found put it back into our equation and solve to see what the corresponding Y will be alright so let's do that putting two back in here for x we'll have 2 squared minus 4 times 2 plus 4 okay order of operations says we got to do that squared stuff first so 2 squared is 4 minus 4 times 2 which would be negative 8 plus 4 ok 4 times negative 8 would be negative 4 plus 4 is going to be equal to 0, so that's the y coordinate of my...

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What is 12 2 solve quadratics?

12 2 solve quadratics refers to the process of finding the values of x that satisfy a quadratic equation in the form ax^2 + bx + c = 0.

Who is required to file 12 2 solve quadratics?

Anyone working on quadratic equations will need to solve for the roots using the formula or methods such as factoring, completing the square, or quadratic formula.

How to fill out 12 2 solve quadratics?

To fill out 12 2 to solve quadratics, you will need to identify the coefficients of x^2, x, and the constant term. Then apply the appropriate method to solve for the values of x.

What is the purpose of 12 2 solve quadratics?

The purpose of solving quadratics is to find the x-intercepts (roots) of the equation, which can provide information about the graph of the quadratic function.

What information must be reported on 12 2 solve quadratics?

The information needed for solving quadratics includes the coefficients of the x^2, x, and constant terms in the quadratic equation.