Question

does the following parabola open upwards or downwards?
$f(x)=(-6x - 8)(-8 + 5x)$
show your work here
\bigcirc opens upwards; has a u shape
\bigcirc opens downwards; has an upside down u shape

Explanation:

Step1: Expand the function

To determine the direction the parabola opens, we first expand the given function \( f(x) = (-6x - 8)(-8 + 5x) \). Using the distributive property (FOIL method):

$$
LATEXBLOCK0
$$

Step2: Simplify the function

Combine like terms:

$$
LATEXBLOCK1
$$

Step3: Determine the leading coefficient

For a quadratic function in the form \( f(x)=ax^2+bx+c \), the sign of the leading coefficient \( a \) determines the direction the parabola opens. If \( a>0 \), the parabola opens upwards; if \( a<0 \), it opens downwards. Here, \( a = -30 \), which is less than 0.

Answer:

Opens downwards; has an upside down U shape