What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function y=−x2−4x+3?

1 Answer
Karthik G · Alan P.
Jan 14, 2016

Vertex: (−2,7)
Axis of symmetry: x=−2
Maximum value : 7
Domain: (−∞,∞)
Range: (−∞,7]

Explanation:

We are given a quadratic function y=−x2−4x+3

On graphing it would graph a parabola.

Since the coefficient of x2 is negative the parabola would be open down.

The x coordinate of vertex would help in finding the axis of symmetry.

For the graph which opens down, there is only maximum and that can be found by the y coordinate of the vertex.

So first let us find the vertex. There are many different approaches to find the vertex.

Let us try one method.

To find the vertex (h,k) we can use the following.

h=−b2a and k=y(h)

h=−−42(−1)

h=4−2

h=−2

k=−(−2)2−4(−2)+3
k=−4+8+3

k=7

Vertex: (−2,7)
Axis of symmetry: x=−2
Maximum value : 7
Domain: (−∞,∞)
Range: (−∞,7]

Check the graph to understand it.

graph{y=-x^2-4x+3 [-10, 10, -5, 8]}

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