Question

1. evaluate the expression ( x^2 + 2x - 10 ) for ( x = -3 )
2. evaluate the expression ( \frac{6x + 4\frac{1}{2}}{x - \frac{1}{2}} ) for ( x = 0 ) and ( y = 3 )
3. determine the equation of the parabola graphed below in vertex form.

graph of a parabola

1. for the graph of ( g(x) ) pictured on the right, over which of the following intervals is ( g(x) ) decreasing?
2. ( -4 < x < 4 )
3. ( -8 < x < -2 )
4. ( -2 < x < 6 )
5. ( -5 < x < 2 )

graph of ( g(x) )

Explanation:

Problem 4 Analysis:

To determine where \( g(x) \) is decreasing, we analyze the graph's slope. A function decreases when, as \( x \) increases, \( y \) (or \( g(x) \)) decreases.

Step 1: Analyze each interval

• Interval 1: \( -4 < x < 4 \)

The graph here likely has mixed behavior (not just decreasing), so this is incorrect.

• Interval 2: \( -8 < x < -2 \)

In this interval, as \( x \) increases (from -8 to -2), the \( y \)-values of the graph decrease (the line is going down from left to right).

• Interval 3: \( -2 < x < 6 \)

Here, the graph is increasing (as \( x \) increases, \( y \) increases), so this is incorrect.

• Interval 4: \( -5 < x < 2 \)

This interval includes both decreasing and increasing parts (e.g., from -5 to -2 it decreases, but from -2 to 2 it may increase), so it’s not purely decreasing.

Answer:

1. \( -8 < x < -2 \)