How do you find the axis of symmetry, and the maximum or minimum value of the function #y=x^2+5x-7#?

1 Answer
Sean
Nov 22, 2017

Axis of symmetry is #x=-2.5#

and

#y_min=-13.5#

Explanation:

This is the equation of a parabola in standard form, i.e.:

#y=ax^2+bx+c#

Here, #a=1, b=5, c=-7#

This parabola opens up as we can see:

graph{x^2+5x-7 [-30.32, 30.32, -15.16, 15.16]}

The axis of symmetry is a vertical line and goes through the vertex. The #x# coordinate of the vertex can be found from:

#x=-b/(2a)=(-5)/(2(1))=-2.5#

Therefore the axis of symmetry is #x=-2.5#

This function does not have a maximum as it goes to infinity on both sides. Its minimum is at its vertex. We can find it by finding the value of #y# at the vertex. We do this by plugging the value of #x# of the vertex into the equation:

#y_min=(-2.5)^2+5(-2.5)-7=6.25-12.5-7=-13.5#

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