Lesson 22

Features of Parabolas

  • Let’s recall what we know about parabolas.

22.1: Matching Quadratic Graphs

Match the equation to the graph. Be prepared to explain your reasoning.

  1. \(y = x^2+x\)
  2. \(y = \text{-}x^2 - 3x\)
  3. \(y = (x-1)(x+5)\)
  4. \(y = x^2 + 5x +1\)

    A

    Parabola facing up with vertex in quadrant 3, near -2 comma -9

    B

    Parabola facing up with vertex in quadrant 3, near -2 comma -5

    C

    Parabola facing down with vertex in quadrant 2, near -2 comma 2.

    D

    Parabola facing up with vertex in quadrant 3, just a little to the left and little below origin 

22.2: Features of a Quadratic Graph

  1. Graph the function \(y = x^2 -10x + 16\).
  2. Find the coordinates for the
    1. \(x\)-intercepts
    2. \(y\)-intercept
    3. vertex
  3. Draw a dashed line along the line of symmetry for the graph.
  4. What do you notice about the line of symmetry as it relates to the:
    1. vertex
    2. \(x\)-intercepts
  5. Use the line of symmetry and the \(y\)-intercept to find another point on the parabola.

22.3: What Do You Know?

  1. Write a function that is represented by a graph with \(x\)-intercepts at \((\text-3,0)\) and \((1,0)\).
    1. Without graphing the function, find the \(y\)-intercept. Explain or show your reasoning.
    2. Without using graphing technology, use the three points you know to sketch the graph of this equation.

      Blank coordinate grid, origin O. X and y axis from negative 8 to 8, by 2s.
    3. What is the \(x\)-coordinate of the vertex? Explain your reasoning.
    4. Using the \(x\)-coordinate you found for the vertex, find the coordinate pair for the vertex.
  2. Graph on x and y axis. Graph goes through points negative 2 comma 0 and 4 comma 0.
    1. What do you know about the coordinates of the \(y\)-intercept?
    2. What do you know about the coordinates of the vertex?

Summary