Question

F(x) = x²+4x+3 A quadratic function is given. (c) Sketch its graph.

Answer 1

To sketch the graph of the quadratic function f(x) = x²+4x+3, find the vertex and y-intercept, determine the direction in which the parabola opens, plot on a coordinate grid, and draw a smooth curve through the points.

Step-by-step explanation:

To sketch the graph of the quadratic function f(x) = x²+4x+3, you would typically follow these steps:

1. Find the vertex of the parabola, which is the point (h, k) where h = -b/(2a) and k is f(h).
2. Determine if the parabola opens upward or downward. Since the coefficient of x² (a) is positive, the parabola opens upward.
3. Identify the y-intercept, which is the point (0, c).
4. Plot these points on a coordinate grid.
5. Draw a smooth curve through these points to complete the sketch of the parabola.

However, the constants provided in the reference are for a different quadratic equation, so we cannot use them directly for this function. To find the vertex for the given function, we calculate h = -4/(2*1) = -2 and evaluate k = f(-2) = (-2)² + 4*(-2) + 3 = 4 - 8 + 3 = -1. Therefore, the vertex is (-2, -1), and the y-intercept is (0, 3).