Question

how to f(x)=-X2-2x-3 sketch the graph of each quadratic function and identify the vertex, domain, range, and the opening of
the graph. State whether the vertex is a minimum or a maximum point, and write the equation of its axis of
symmetry
(x) = x
Vertex
Opening of the graph:
Vertex is a
point
Equation of the axis of symmetry:
Domain:
Range:​

Answer 1

Given: $f(x)=-x^2-2x-3$

To find:

Graph of quadratic function and identify the vertex, domain, range, and the opening of

the graph. State whether the vertex is a minimum or a maximum point, and write the equation of its axis of symmetry (x) = x

Vertex:

Opening of the graph:

Vertex is at point:

Equation of the axis of symmetry:

Domain:

Range:

Solution:

Step 1: Graph the function.

Put values of x and calculate values of f(x).

Graph is attatched.

Step 2: Write the vertex, axis of symmetry and other information from graph.

Vertex:

$( - 1,- 2)$

Axis of symmetry: y-axis

Equation of the axis of symmetry:

$x + 1 = 0$

Opening of the graph: Downwards

Towards negative y-axis.

Step 3: Find domain and range of function.

Domain of function is complete real number;

Domain

$f(x) = - \infty \: to \: \infty$

Range:

$f(x) = - \infty \: to \: - 2$

because for any value of x, function should not take value beyond -2.

Final answer:

1) Vertex:$(- 1, - 2)$

2) Axis of symmetry: y-axis

3) Equation of axis of symmetry:$x + 1 = 0$

4)Opening : Negative y-axis

5) Domain:$( - \infty, \: \infty)$

6) Range:$( - \infty, \: - 2]$

Hope it helps you.

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