Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 7

Chapter 2, Problem 7

In Exercises 6–8, use the graph and determine the x-intercepts if any, and the y-intercepts if any. For each graph, tick marks along the axes represent one unit each.

Verified step by step guidance

Observe the graph of the quadratic function provided. The x-axis and y-axis are labeled, and tick marks represent one unit each.

To find the x-intercepts, look for the points where the graph crosses the x-axis. These are the points where the y-value is 0.

From the graph, identify the x-coordinates of the points where the curve intersects the x-axis. These are the x-intercepts.

To find the y-intercept, look for the point where the graph crosses the y-axis. This is the point where the x-value is 0.

From the graph, identify the y-coordinate of the point where the curve intersects the y-axis. This is the y-intercept.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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 a quadratic function, this is simply the constant term when the function is expressed in standard form.

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 identifying intercepts and analyzing the function's behavior.

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