Quadratics Question 3

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?

y=3x^2-11x-20

y=3x^2+11x-20

y=4x^2-17x-15

y=4x^2+17x-15

y=15x^2-17x-4

Approach 1

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}

Approach 2

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.