The first stage is to factorise the equation, since x2 is negative I will multiply the equation by −1 to make it easier to factorise.
Factorise:
y=x2−4x−12
(x−6)(x+2)
To obtain the x-intercept we need to make y=0,
0=(x−6)(x+2)
We can now solve for the two values
x1−6=0
x1=6
x2+2=0
x2=−2
To obtain the axis of symmetry for the parabola we add the two x values together then divide by 2. This will give the x value for the vertex.
xv=x1+x22=6−22=2
Now to get the y value for the vertex substitute x=2 into the original equation and solve:
yv=−x2+4x+12
yv=(2)2−4(2)−12
yv=16
Therefore the vertex is (2,16)
The final intercept we need is the y-intercept, this can be calculated by substituting x=0 into the original equation:
y=−x2+4x+12
y=−(0)2+4(0)+12
y=12
y-intercept = (0,12)
