How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y = x^2 + 4x - 5 #?

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Answer 1 · 2017-05-10T17:33:41

#y_min=-9#

Axis of symmetry #x=-2#

we first of all need to complete the square before we find the required information.

#y=x^2+4x-5#

#y=(x^2+4x)-5#

half the coefficient of x , square it; then add and subtract it

#y=(x^2+4x+color(blue)(2^2))-5-color(blue)(2^2#

The bracket is now a perfect square

#y=(x+2)^2-9#

because the graph is #+x^2# we will have a minimum.

This minimum occurs at the vertex
ie when #(x+2)=0#

so minimum occurs at #x=-2=>y_min=-9#

The axis of symmetry is the line through the vertex

ie.#" "x=-2#

graph{x^2+4x-5[-7,5,-12,5]}

(The scale of the graph is set to show intersection points - it won't look like this on graph paper!!!)