Algebra 1, Please Help! Graphs of Function in Standard and Factored Forms

Question

The equations  y=x²+x−20 and y = (x−4)(x+5) both define the same quadratic function.

Identify the x- and y-intercepts of the function. Explain how you know from looking at the equations.

Answer 1

By using the first equation, you can easily find the y intercept by setting x = 0, then you can see that y = -20. The y-intercept is -20.

Since the second equation is in factored form, you can use it to find the x-intercepts. Set y = 0, then you can see that in order for the product to be zero either factor has to be zero. Thus set x - 4 = 0 and you get x = 4, then x + 5 = 0 obtains x = -5. The x-intercepts are 4 and -5.

Vahan