Domanda del libro di testo
Find all values of x satisfying the given conditions. y = 2x2 - 3x and y = 2
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 111a
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = - (x + 1)2 + 4
Guida verificata passo dopo passo1
To find the x-intercepts of the graph, set y = 0 in the given equation. The equation becomes 0 = - (x + 1)^2 + 4.
Rearrange the equation to isolate the squared term: (x + 1)^2 = 4.
Take the square root of both sides, remembering to include both the positive and negative roots: x + 1 = ±√4.
Simplify the square root: x + 1 = ±2. This gives two equations: x + 1 = 2 and x + 1 = -2.
Solve each equation for x: For x + 1 = 2, subtract 1 to get x = 1. For x + 1 = -2, subtract 1 to get x = -3. The x-intercepts are x = 1 and x = -3.
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X-Intercept
The x-intercept of a graph is the point where the graph intersects the x-axis. This occurs when the value of y is zero. To find the x-intercept, you set the equation equal to zero and solve for x. In the given equation, this means solving - (x + 1)^2 + 4 = 0.
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Graphing Intercepts
Quadratic Functions
The equation provided is a quadratic function, which is typically in the form y = ax^2 + bx + c. Quadratic functions produce parabolic graphs, which can open upwards or downwards depending on the sign of 'a'. In this case, the negative sign indicates the parabola opens downwards, affecting the location of the x-intercepts.
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06:36Solving Quadratic Equations Using The Quadratic Formula
Graphing Techniques
Understanding how to graph a quadratic function involves identifying key features such as the vertex, axis of symmetry, and intercepts. The vertex can be found using the formula x = -b/(2a), and the intercepts help in sketching the graph accurately. This knowledge is essential for matching the equation to its corresponding graph.
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02:16Graphs and Coordinates - Example
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Domanda del libro di testo
In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x2 - 2x + 2
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