Given the function ƒ(x) = x 2 - 4x - 5 Identify the zeros using factorization. Draw a graph of the function. Its vertex is at (2, -9).
Answers
This equation is a parabola in general form. The easiest way to graph it is to convert it to standard form, y=a(x-p)^2 + q. You can do this by completing the square:
Halve the b term (b=4 in your equation) and then square it: (4/2)^2 = 2^2 = 4
Add this number to the first 2 terms, but then subtract it at the end (so that you are just adding zero to the overall equation):
y=x^2 +4x + 4 + 3 - 4
y=(x^2+4x+4) +3-4
y=(x+2)^2 -1
Now the equation is in standard form, y=a(x-p)^2 + q. The vertex is at (p,q)=(-2,-1).
You can find the y=intercept by setting x=0 and solving for y. It's easiest to do this with the general form:
y=x^2+4x+3
y = 0+)+3
y=3
The y-intercept is y=3.
To find the x-intercepts, factor, set y=0 and solve for x. You have to solve by factoring:
y=x^2+4x+3
0 = x^2+4x+3
0 = (x+3)(x+1)
Which means that the x-intercepts are x= -3, and x= -1.
You now know the x-intercepts, y-intercept, and vertex. You should be able to just connect the dots to graph the equation.