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

Question

Avery Alexander · Accepted Answer

#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!!!)

Isaiah Anthony · Answer

undefined To find the axis of symmetry, use the formula x = -b/2a, where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c.

For the function y = x^2 + 4x - 5, the axis of symmetry is x = -b/(2a) = -4/(2*1) = -2.

To graph the function, plot points using values of x and find corresponding y values using the equation.

To find the maximum or minimum value, determine whether the coefficient of x^2 (a) is positive or negative. If a is positive, the vertex is the minimum point, and if a is negative, the vertex is the maximum point. In this case, since a = 1 (positive), the vertex represents the minimum value.

To find the y-coordinate of the vertex, substitute the x-coordinate of the axis of symmetry into the function.

For y = x^2 + 4x - 5, the vertex occurs at x = -2. Substituting x = -2 into the equation gives y = (-2)^2 + 4(-2) - 5 = -1.

So, the axis of symmetry is x = -2, the vertex is (-2, -1), and the minimum value of the function is -1.