Question

What is the vertex of x^2 + 4x - 12

Answer 1

`(-2, -16)\\`

Step-by-step explanation:

The vertex of a quadratic function which gets plotted as a parabola is either the minimum or maximum (x, y) value of that function.

The following rule applies to finding the x value of the vertex

`\mathrm{The\:vertex\:of\:an\:up-down\:facing\:parabola\:of\:the\:form}\:\\y=ax^2+bx+c\:\mathrm{is}\:x_v=-(b)/(2a)`

The equation is

`y=x^2+4x-12`

`\textrm {Here }\\a = 1, b = 4, c= -12\\\\`

`So\; x_v, \textrm{ the x value of the vertex } = -(4)/(2\cdot \:1) = -2\\\\\textrm {Plug this value of x into the equation to find the y-value of the vertex}\\`

`y_v=\left(-2\right)^2+4\left(-2\right)-12\\\\\\y_v = 4 -8 - 12 = -16\\\\`

`\mathrm{Therefore\:the\:parabola\:vertex\:is}\\(-2, -16)`