Which of the following could be the equation of the graph in the xy-pl

Using the standard form of the equation for a parabola, we need three points. We have them: (-5,0), (4,0), and (0,-60)

(1)Standard form of equation for a parabola:
\(y=a(x-b)(x-c)\)

(2) Use the roots \(x=-5, x=4\) from points \((-5,0)\) and \((4,0)\)
(when \(y=0\), \(x=-5\) and \(x=4\))

(3) Replace \(b\) and \(c\) with the roots:
\(y=a(x+5)(x-4)\)

(4) Find \(a\) with a third point's coordinates. We have the y-intercept: when \(x=0\), \(y= -60\). That's the third point we need to find \(a\)

Plug the point \((0,-60)\) into the equation:
\(-60=a(0+5)(0-4)\)
\(-60=a(5)(-4)\)
\(-60=-20a\)
\(a=3\)

(5) Simplify the equation
\(y=3(x+5)(x-4)\)
\(y=(3x+15)(x-4)\)
\(y=3x^2+3x-60\)

Answer E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.