Final answer:
To graph a quadratic function, plot the vertex and intercepts, and draw a U-shaped curve. The axis of symmetry is found with x = -b/2a. The domain is all real numbers, and the range is determined by the vertex and the direction the parabola opens.
Step-by-step explanation:
To sketch the graph of a quadratic function using the vertex and intercepts, first plot the vertex of the parabola, which is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. Then, find the x-intercepts (where the parabola crosses the x-axis) by setting the function f(x) equal to zero and solving for x. Similarly, find the y-intercept by evaluating f(0). Connect the intercepts and the vertex with a smooth, U-shaped curve.
The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two symmetric halves. For a quadratic function in the form of f(x) = ax2 + bx + c, the axis of symmetry can be given by the equation x = -b/2a.
The domain of any quadratic function is all real numbers because you can substitute any real number for x and get a result for f(x). The range, however, depends on the vertex's y-coordinate and whether the parabola opens upwards or downwards. If it opens upwards, the range includes all real numbers greater than or equal to the y-coordinate of the vertex. If it opens downwards, the range includes all real numbers less than or equal to the y-coordinate of the vertex.