Question

does the following parabola open upwards or downwards?
$f(x) = \frac{3}{5}x^2 + 3x + 4$
show your work here
\bigcirc opens upwards, has a u shape
\bigcirc opens downwards, has an upside down u shape

Explanation:

Step1: Recall parabola form

The standard form of a quadratic function (parabola) is \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants.

Step2: Determine sign of \( a \)

For the function \( f(x) = \frac{3}{5}x^2 + 3x + 4 \), the coefficient of \( x^2 \) (i.e., \( a \)) is \( \frac{3}{5} \). Since \( \frac{3}{5} > 0 \), the parabola opens upwards (has a U - shape).

Answer:

Opens upwards; has a U shape