Answer:
The equation in standard form is: [tex]y=2x^2-2x-24[/tex]
Step-by-step explanation:
Since they give you the x-intercepts (the zeros of the quadratic expression) one knows that the binomials: (x-(-3)) and (x-4) must be factors of the quadratic expression.
We can therefore write the equation as:
[tex]y=k\,(x+3)(x-4)[/tex]
using the binomial factors given above, and a numerical factor "k" that we can determine by using the information that the graph passes through the point (2,-20):
[tex]y=k\,(x+3)(x-4)\\-20=k\,(2+3)(2-4)\\-20=k\,(5)(-2)\\-20=k\,(-10)\\k=\frac{-20}{-10} \\k=2[/tex]
Then,the equation can be written as:
[tex]y=2\,(x+3)(x-4)\\y=2(x^2-x-12)\\y=2x^2-2x-24[/tex]
where we wrote the equation already in standard form
