Question

If there is more than one intercept , separate them with commas I only need the VERTEX , I have the x intercept

Answer 1

vertex is (-2, -16)

Step-by-step explanation:
`y=x^2+\text{ 4x - 12}`

Vertex is given as (h, k)

To get the vertex, we will apply the formula:

h = -b/2a

k = f(-b/2a)

`\begin{gathered} \text{From the equation:} \\ a\text{ = 1, b = 4, c = -12} \\ h\text{ = }(-b)/(2a)\text{ = }(-4)/(2(1)) \\ h\text{ = -4/2} \\ h\text{ = -2} \end{gathered}`
`\begin{gathered} k\text{ = f(-b/2a)} \\ y\text{ = f(x)} \\ f(x)=x^2+4x\text{ - 12} \\ f((-b)/(2a))\text{ = f(-2) } \\ \text{ As -b/2a = -2, we will be substituting x in the function with -2 } \\ \\ f(-2)=(-2)^2+4(-2)\text{- 12} \\ f(-2)\text{ = 4 - 8 - 12} \\ \text{f(-2) = -16} \\ k\text{ = -16} \end{gathered}`

Hence, the vertex (h, k) is (-2, -16)