Blog

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?

Which is an alternate form of \( x^3 + y^3 \), creating a polynomial identity?

A radioactive substance loses 30% of its mass each year.   Which type of sequence represents the remaining mass each year?

A bacteria culture starts with 400 cells and doubles every hour.   What type of sequence models the number of cells over time?

A sequence is shown below:   Data Table \(n\) 1 2 3 4 \(a_n\) 3 9 27 81   Which type of sequence is represented?