option A
Explanation:
To detrmine the correct graph, let's find the factors of the function given:
[tex]\begin{gathered} y=x^2\text{ + 4x - 12} \\ \text{The factors of -12 whose sum gives +4 are +6 and - 2} \end{gathered}[/tex][tex]\begin{gathered} y=x^2\text{ + 6x - 2x - 12} \\ y\text{ = x(x + 6) -2(x + 6)} \\ y\text{ = (x - 2) (x + 6)} \end{gathered}[/tex]
To get the factors equate the function to zero, that is y = 0
[tex]\begin{gathered} 0\text{ = (x -2)(x+6)} \\ x-2\text{ = 0 or x + 6 = 0} \\ x\text{ = 2 or x = -6} \end{gathered}[/tex]
The graph with two x intercepts as 2 and -6 will be the correct quadratic function
Each unit on the graph is 4 units
From the options, option A has x intercepts as 2 and -6
