One of the following equations is that of a parabola with \(x\)-intercepts \(-5\) and \(\dfrac{3}{4}\) in the standard \((x,y)\) coordinate plane. Which equation?

Summary Submit Skip Question

Given the intercepts, we can write an equation with the following factors:

$$ y=(x+5)\left(x-\frac{3}{4}\right) $$

There are no fractional terms in the answer choices, so we can manipulate the second factor:

$$ y=(x+5)(4x-3) $$ $$ y=4x^2+20x-3x-15 $$ $$ \boxed{y=4x^2+17x-15} $$

Although it can take some time, you can just plug in each equation into your calculator and find the ones with the correct \(x\)-intercepts.