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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 46a
Capitolo 2, Problema 46a

Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.

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Step 1: Observe the graph of the quadratic function provided. The graph is a parabola that opens upwards, and the tick marks along the axes represent one unit each.
Step 2: To determine the x-intercepts, locate the points where the graph crosses the x-axis. These are the points where the y-value is zero. From the graph, identify the x-coordinates of these points.
Step 3: To determine the y-intercept, locate the point where the graph crosses the y-axis. This is the point where the x-value is zero. From the graph, identify the y-coordinate of this point.
Step 4: Verify the intercepts by checking the coordinates visually on the graph. Ensure that the x-intercepts and y-intercept align with the tick marks provided.
Step 5: Summarize the intercepts: The x-intercepts are the points where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis.

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X-Intercepts

X-intercepts are the points where a graph crosses the x-axis. At these points, the value of y is zero. To find the x-intercepts of a function, you set the function equal to zero and solve for x. In the context of a quadratic function, this often involves factoring or using the quadratic formula.
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Graphing Intercepts

Y-Intercepts

Y-intercepts are the points where a graph crosses the y-axis. At these points, the value of x is zero. To determine the y-intercept of a function, you evaluate the function at x = 0. For quadratic functions, this is simply the constant term when the function is expressed in standard form.
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Graphing Intercepts

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'. Understanding the shape and properties of parabolas is essential for analyzing their intercepts.
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Solving Quadratic Equations Using The Quadratic Formula
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In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. (x - 4)/6 ≥ (x - 2)/9 + 5/18

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