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How many times does the graph of \( f(x) = x^4 – 6x^2 + 9 \) cross the x-axis? 

Which function matches the graph? The x-axis spans from just below zero to above 4, and the y-axis spans from just below zero to above 4. Both axes have a scale of 2 in increments of 0.5. The purple parabolic function opens upward and has a minimum vertex at (2, 1). The parabola is symmetric around the vertical line passing through the vertex. It passes through the coordinates (1, 4) and (3, 4) and extends out of view. 

A sequence is defined by \(a_n = 250(0.7)^n\).   What type of sequence does this represent?

An environmental scientist is modeling the population range of a protected species in a wildlife preserve. The population density (in animals per square kilometer) depends on the distance (in kilometers) from a central water source. Two constraints are used in the model: The minimum healthy population density at various distances is modeled by The maximum sustainable population density at various distances (due to food and space) is modeled by   This system, shown graphically below, represents the acceptable population levels within the preserve. Which statement below reflects a solution to this system, in context? “The x-axis spans from below zero to 6, and the y-axis spans from negative 4 to 4. Both axes have a scale of 2 in increments of 0.5. A dashed black parabola opens upward, enclosing a gray-shaded parabolic region above it. The vertex of this parabola is at (3, negative 1), while it passes through the x-axis at (2, 0) and (4, 0). Another solid green parabola opens downward and encloses a light green parabolic region below it. The vertex of this parabola is at (2, 1), while it passes through the x-axis at (1, 0) and (3, 0). The two parabolic regions overlap, forming a dark green-gray region in the middle of the graph where the two curves intersect at approximately (1.6, 0.9) and again at approximately (3.8, -0.8)”

The graph below shows a system that includes a quadratic and a linear function. The parabola opens upward and intersects the line at two points. Which of the following systems of equations best matches the graph? The x-axis spans from below zero to just above 4, and the y-axis spans from negative 2 to just above 4. Both axes have a scale of 2 in increments of 0.5.   The purple parabola opens upward, with its vertex located at the coordinate (1.5, negative 0.5). It has x intercepts at (1,0) and (2,0), and the y-intercept at (0, 2), while passing through the coordinate (3, 2). The blue line has a positive slope, crossing the x-axis at (2, 0) and the coordinate (3, 2), extending upward. The two graphs intersect at (2,0) and (3, 2). 

Rewrite the equation in standard form and identify the conic:   \(x^2 – 10x + y – 1 = 0\)

What are the center and radius of the circle given by \(x^2+y^2-10x+2y+13=0\(?

Write the equation of the circle given by \(x^2+y^2+6x+12y+20=0\).

If \( P(x) = x^2 + 3x – 4 \) and \( Q(x) = 2x^2 – x + 1 \), what is \( P(x) + Q(x) \)?

A population model is given by \(f(n) = 40(1.4)^{n-1}\).   Does the infinite series \(\sum_{n=1}^{\infty} f(n)\) have a finite sum?