#Factor of a quadratic equation how to

If there is a limited amount of space and we desire the largest monitor possible, how do we decide which one to choose? In this section, we will learn how to solve problems such as this using four different methods.Īn equation containing a second-degree polynomial is called a quadratic equation. Proportionally, the monitors appear very similar. The left computer monitor in the image below is a 23.6-inch model and the one on the right is a 27-inch model.

Use the discriminant to determine the number and type of solutions to a quadratic equation.Use the quadratic formula to solve a quadratic equation.Complete the square to solve a quadratic equation.Use the Pythagorean Theorem and the square root property to find the unknown length of the side of a right triangle.Use the square root property to solve a quadratic equation.Factor a quadratic equation to solve it.By the end of this section, you will be able to: Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. We can see this by expanding out the general form and setting it equal to the standard form. The standard form and the general form are equivalent methods of describing the same function. But if | a | 1, | a | > 1, so the graph becomes narrower. If h > 0, h > 0, the graph shifts toward the right and if h 1, | a | > 1, the point associated with a particular x - x - value shifts farther from the x-axis, so the graph appears to become narrower, and there is a vertical stretch. If k > 0, k > 0, the graph shifts upward, whereas if k 0, k > 0, so the graph is shifted 4 units upward. The x - x - intercepts, those points where the parabola crosses the x - x - axis, occur at ( −3, 0 ) ( −3, 0 ) and ( −1, 0 ). For a parabola that opens upward, the vertex occurs at the lowest point on the graph, in this instance, ( −2, −1 ). The vertex always occurs along the axis of symmetry. This also makes sense because we can see from the graph that the vertical line x = −2 x = −2 divides the graph in half. The axis of symmetry is x = − 4 2 ( 1 ) = −2. If a 0, a > 0, the parabola opens upward. If a > 0, a > 0, the parabola opens upward. Where a, b, a, b, and c c are real numbers and a ≠ 0. These features are illustrated in Figure 2.į ( x ) = a x 2 + b x + c f ( x ) = a x 2 + b x + c The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry. In either case, the vertex is a turning point on the graph. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. One important feature of the graph is that it has an extreme point, called the vertex. Example: Solve 6m 2 7m + 2 0 by factoring method. This method of solving quadratic equations is called factoring the quadratic equation. We can write the quadratic equation as a product of factors having degree less than or equal to two. The graph of a quadratic function is a U-shaped curve called a parabola. Solving Quadratic Equations By Factorisation. Working with quadratic functions can be less complex than working with higher degree functions, so they provide a good opportunity for a detailed study of function behavior. In this section, we will investigate quadratic functions, which frequently model problems involving area and projectile motion. The cross-section of the antenna is in the shape of a parabola, which can be described by a quadratic function. (credit: Matthew Colvin de Valle, Flickr)Ĭurved antennas, such as the ones shown in Figure 1, are commonly used to focus microwaves and radio waves to transmit television and telephone signals, as well as satellite and spacecraft communication.

Factor of a quadratic equation