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

1. Observe the graph of the quadratic function provided. The x-axis and y-axis are labeled, and tick marks represent one unit each.
2. 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.
3. From the graph, identify the x-coordinates of the points where the curve intersects the x-axis. These are the x-intercepts.
4. 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.
5. From the graph, identify the y-coordinate of the point where the curve intersects the y-axis. This is the y-intercept.

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, one typically sets the function equal to zero and solves for x. In the context of a quadratic function, this can involve factoring, using the quadratic formula, or completing the square.

Y-Intercepts

Y-intercepts are the points where a graph crosses the y-axis, which occurs when the value of x is zero. To determine the y-intercept of a function, one evaluates 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.