How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=x^2+4x-1?

2 Answers
Feb 11, 2016

Explanation is given below.

Explanation:

y=x^2+4x-1

To solve such problems, go for completing the square. If not then find vertex using h=-b/(2a) and k by substituting the x=h in the given equation.

The x=h would be the axis of symmetry. If the graph opens up there would be a minimum. If the graph opens down then there would be a maximum.

The coefficient of x^2 is positive then the graph opens up as is the case in this problem that means we have a minimum value and that value is k value of the vertex.

Let me show it by completion of square.

y=x^2+4x-1
I would first add 1 to both sides, this is done to keep x^2+4x on one side which we would convert to a perfect square.

y+1=x^2+4x-cancel(1)+cancel(1)
y+1=x^2+4x

Next step is to take the coefficient of x and divide it by 2. Square the result and add both sides.

y+1+(4/2)^2=x^2+4x+(4/2)^2
y+1+(2)^2=x^2+4x+2^2
y+1+4=(x+2)^2
y+5=(x+2)^2
Subtract 5 both the sides we get
y+cancel(5)-cancel(5)=(x+2)^2-5

y=(x+2)^2-5 Vertex form

Vertex (-2,-5)
Axis of symmetry x=-2
Minimum at (-2,-5) the minimum value is -5

Feb 11, 2016

Plot the graph using Graph tool given above.

Explanation:

graph{y=x^2+4x-1 [-20, 20, -10, 10]}
From the Graph:
Vertex is located at (−2,−5)
Axis of symmetry x=−2
Minimum at (−2,−5).