In Exercises 41–46, 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.

Verified step by step guidance

1. Observe the graph to identify the points where the curve intersects the x-axis. These points are the x-intercepts.
2. Note that the x-intercepts are the points where the y-value is zero.
3. From the graph, determine the x-coordinates of the points where the curve crosses the x-axis.
4. Next, identify the point where the curve intersects the y-axis. This point is the y-intercept.
5. Note that the y-intercept is the point where the x-value is zero. From the graph, determine the y-coordinate of this point.

Key Concepts

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 quadratic functions, 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 analyzing their intercepts.