Question

1) Graph the quadratic function given in standard form and identify the key features. Include at least 5 points on your

graph.
y = -x2 - 2x + 1
Axis of Symmetry:
Vertex:
Y-intercept:
Domain:
Range:

Answer 1

Please find attached the graph of the quadratic function is created using Microsoft Excel

1) The line of symmetry is x = -1

2) The vertex is (-1, 2)

3) The y-intercept is (0, 1)

4) The domain is -∞ ≤ x ≤ ∞

5) The range is 2 ≥ y ≥ -∞

Explanation:

The given equation is y = -x² - 2·x + 1

The general vertex form is y = a·(x - h)² + k

h = -b/(2·a) = 2/(-2) = -1

k = f(h) = -(-1)² - 2×(-1) + 1 = 2

Therefore;

1) The line of symmetry goes through the vertex and the line of symmetry is x = -1

2) The vertex = (h, k) = (-1, 2)

3) The y-intercept is the coordinate of the point where x = 0 which is (0, 1)

4) The domain are the possible x-values, therefore, the domain = -∞ ≤ x ≤ ∞

5) The range is the possible values y-values.

From the graph, we have the range = 2 ≥ y ≥ -∞

The graph of the quadratic function is created using Microsoft Excel by generating y-values based on the equation and using the graphing function to insert a two dimensional graph of the generated combination of x and y values as shown in the attached figure.