Quadratic Function Practice Problems & Solutions

The function is positive when it is above the X-axis.

Let's note that the intersection point of the graph with the X-axis is:

$(2,0)$ meaning any number greater than 2:

$x > 2$

The function we see is a decreasing function,

Because as X increases, the value of Y decreases, creating the slope of the function.

We know that this function intersects the X-axis at the point x=-4

Therefore, we can understand that up to -4, the values of Y are greater than 0, and after -4, the values of Y are less than zero.

Therefore, the function will be positive only when

X < -4

In the exercise, we have an inequality equation.

We treat the inequality as an equation with the sign -=,

And we only refer to it if we need to multiply or divide by 0.

 $10x-4 ≤ -3x-8$

We start by organizing the sections:

$10x+3x-4 ≤ -8$

$13x-4 ≤ -8$

$13x ≤ -4$

Divide by 13 to isolate the X

$x≤-\frac{4}{13}$

Let's look again at the options we were asked about:

Answer A is with different data and therefore was rejected.

Answer C shows a case where X is greater than$-\frac{4}{13}$, although we know it is small, so it is rejected.

Answer D shows a case (according to the white circle) where X is not equal to$-\frac{4}{13}$, and only smaller than it. We know it must be large and equal, so this answer is rejected.

Therefore, answer B is the correct one!

To solve this problem, we need to determine the slope of the line depicted on the graph.

First, understand that the slope of a line on a coordinate plane indicates how steep the line is and the direction it is heading. Specifically:

• A positive slope means the line rises as it goes from left to right.
• A negative slope means the line falls as it goes from left to right.

Let's examine the graph given:

• We see that the line starts at a higher point on the left and descends to a lower point on the right side.
• As we move from the left side of the graph towards the right, the line goes downwards.

This downward trajectory clearly indicates a negative slope because the line is declining as we move horizontally left to right.

Therefore, the slope of this function is Negative.

The correct answer is, therefore, Negative slope.

To determine the slope of the line shown on the graph, we perform a visual analysis:

• We examine the orientation of the line from left to right.
• The red line starts at a higher point on the left and descends to a lower point on the right.
• This indicates a downward movement, which corresponds to a negative slope.

Therefore, by observing the direction of the line, we conclude that the slope of the function is negative. This positional evaluation confirms that the correct answer is negative slope.