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Chapter #10: Quadratic Functions Review Sheet

(Questions #1-3) Write each formula:

  1. Axis of symmetry
  1. y-intercept
  1. Quadratic Formula

(Questions #4-5) Describe, in words, how to:

  1. Find the vertex algebraically
  1. Solve a system of equations graphically
  1. Using the equation to represent a parabola which statement is true?Explain.

(1) If b is negative, the parabola opens downward.

(2) Ifa is negative, the parabola opens upward.

(3) Ifa is positive, the parabola opens upward.

(4) If c is negative, the parabola opens downward.

  1. A function is written in vertex form as

. If the parent function is describe the transformations that occurred to produce the graph of

Given the function find each of the following algebraically:

  1. Roots, in simplest radical form.
  1. Axis of symmetry
  1. Turning point, and describeit as a maximum or minimum
  1. y-intercept
  1. How many solutions are there for this linear-quadratic system of equations? Explain.
  1. Use your calculator to find the solution set of rounded to the nearest hundredth.
  1. The graph below shows the curves that are listed.

Write the number of the equation of each beside its curve.Explain your reasoning.

(1)

(2) 2

(3)

(4)

(5)

  1. What are the coordinates of the turning point of the quadratic function,, shown below?

Show all work for this section.Partial credit is awarded on the test.

  1. Solve algebraically and leave your answer in simplest radical form.
  1. Identify the turning point of the function by writing it in vertex form.

Show all work for this section. This includes all work, tables, and labels.

  1. Amy tossed a ball in the air in such a way that the path of the ball was modeled by the equation

. In the equation, y represents the height of the ball in feet and x is the time in seconds.

a) Graph for on the grid provided

b) At what time, x, is the ball at its highest point?

  1. Solve the system graphically.

Answers:

  1. Use , then plug that number into the given equation to find y
  2. Solve each for y, graph each using tables, state the intersection point
  3. 3, Explain
  4. Left 4, down 2
  5. x = -1
  6. (-1, -7)
  7. (0, -5)
  8. one solution
  9. {-1.55, 0.22}
  1. See picture
  1. (-5, -6)
  2. a) Show table for graph

b) 3

  1. Solutions: