Applying the Quadratic Formula (Part 1)
1) Select the equations that have 2 solutions. Write each corresponding letter in the answer box and separate letters with commas.
a) b) c) d) e)
A frog jumps in the air. The height, in inches, of the frog is modeled by the function , where is the time after it jumped, measured in seconds.
2) Solve .
3) What do the solutions tell us about the jumping frog?
A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation where is measured in seconds since the ball was thrown.
4) Find the solutions to the equation .
5) What do the solutions tell us about the tennis ball?
Rewrite each quadratic expression in standard form.
Find the missing expression in parentheses so that each pair of quadratic expressions is equivalent. Then, show that your expression meets this requirement.
11) Show that your expression makes the pair equivalent.
13) Show that your expression makes the pair equivalent.
15) Show that your expression makes the pair equivalent.
The number of downloads of a song is a function, , of the number of weeks, , since the song was released. The equation defines this function.
16) What does the number 100,000 tell you about the downloads?
17) What about the ?
18) Is meaningful in this situation?
19) Explain your reasoning.
Consider the equation .
Identify the values of , , and that you would substitute into the quadratic formula to solve the equation.
Evaluate each expression using the values of , , and .
31) The solutions to the equation are and . Do these match the values of the last expression you evaluated in the previous question?
Describe the graph of .
32) Does it open upward or downward?
33) Where is its y-intercept?
34) What about its x-intercept?
Without graphing, describe how adding to would change each feature of the graph of . (If you get stuck, consider writing the expression in factored form.)
35) the x-intercepts
36) the vertex
37) the y-intercept
38) the direction of opening of the U-shape graph