Question

does the following parabola open upwards or downwards?
$f(x) = -\frac{7}{8}(x - 5)^2 + 2$
show your work here

○ opens upwards; has a u shape
○ opens downwards; has an upside down u shape

Explanation:

Step1: Recall the vertex form of a parabola

The vertex form of a parabola is \( f(x) = a(x - h)^2 + k \), where \( (h, k) \) is the vertex and \( a \) determines the direction of opening.

Step2: Identify the value of \( a \) in the given function

In the function \( f(x) = -\frac{7}{8}(x - 5)^2 + 2 \), the value of \( a \) is \( -\frac{7}{8} \).

Step3: Determine the direction of opening

If \( a > 0 \), the parabola opens upwards (U - shape). If \( a < 0 \), the parabola opens downwards (upside - down U - shape). Since \( -\frac{7}{8}<0 \), the parabola opens downwards.

Answer:

Opens downwards; has an upside down U shape