Test Review Time!

Hey everyone! This post is designed to help you ace your upcoming test. Below, you'll find the review packet that we worked on together in class, complete with solutions. Your test will cover similar concepts but with a slightly reduced number of problems. Make sure you understand each problem type in the packet and you'll be well-prepared!

Key Concepts to Review:

  • Graphing Polynomials: You'll need to be comfortable graphing polynomials using tables of values. This includes understanding how to plot points and connect them to form the graph.
  • Identifying Graph Types: Be able to identify whether a graph is linear, quadratic, or cubic based on its shape and equation. Remember that:
    • Linear functions have the form $y = mx + b$ and graph as a straight line.
    • Quadratic functions have the form $y = ax^2 + bx + c$ and graph as a parabola.
    • Cubic functions have the form $y = ax^3 + bx^2 + cx + d$ and have a more complex curve.
  • Determining the Degree: The degree of a polynomial is the highest power of the variable. For example:
    • $y = 2x + 3$ has a degree of 1 (linear).
    • $y = x^2 + 4x + 3$ has a degree of 2 (quadratic).
    • $y = x^3 - 1$ has a degree of 3 (cubic).
  • Even vs. Odd Degree: The degree of a polynomial affects its end behavior. Remember these basic rules:
    • Even Degree: If the degree is even, the ends of the graph point in the same direction (both up or both down).
    • Odd Degree: If the degree is odd, the ends of the graph point in opposite directions (one up and one down).
  • End Behavior: Describe what the graph does as $x$ approaches positive or negative infinity. This is related to the leading coefficient and the degree of the polynomial. For example, for $y = x^2$, as $x \rightarrow \infty$, $y \rightarrow \infty$ and as $x \rightarrow -\infty$, $y \rightarrow \infty$.
  • Maximum and Minimum Values: Identify if the graph has a maximum (highest point) or a minimum (lowest point). For parabolas, this is called the vertex. For cubic functions, there can be local maximums and local minimums. Make sure you give coordinates as an ordered pair $(x, y)$.
  • Intercepts: Identify the y-intercept (where the graph crosses the y-axis) and the x-intercept(s) (where the graph crosses the x-axis).
    • The y-intercept occurs when $x=0$.
    • The x-intercept(s) occur when $y=0$.

Packet Review:

Go through each problem in the packet carefully. Pay special attention to:

  • Graphing the function from a table of values.
  • Identifying the type of graph (linear, quadratic, cubic).
  • Finding the degree of the polynomial.
  • Describing the end behavior.
  • Locating maximum and minimum points.
  • Finding the x and y intercepts.

Good luck studying! I'm confident you'll do great on the test! Remember to get a good night's sleep and come prepared to show what you know!