A video game designer decides to include a character in a newgame that only moves along a parabolic path. The designer uses thefunction x²+50+10 to model this character’s path, where y is theheight of the character in pixels and x is the time in seconds thatit takes the character to move across one parabolic path.
a. Is the vertex of the function a maximum or minimum point and howcan you tell?
b. Find the x-coordinate of the vertex. Show all work leading toyour answer and write the answer in simplest form.
c. Find the y-coordinate of the vertex. Show all workleading to your answer and write the answer in simplest form.
d. Write the vertex as an ordered pair (x, y). What does the vertexrepresent for this situation? Write 1-2 sentences to explain youranswer.
2. A satellite dish has the shape of a parabola, the U-shaped graphof a quadratic function. Suppose an engineer has determined thatthe shape of one of the satellite dishes offered by the company canbe modeled by the quadratic function y=2/27x²-4/3x , where y is thevertical depth of the satellite dish in inches and x is thehorizontal width in inches.
a. Is the vertex of the function a maximum or minimum point and howcan you tell?
b. Find the x-coordinate of the vertex. Show all work leading toyour answer and write the answer in simplest form.
c. Find the y-coordinate of the vertex. Show all workleading to your answer and write the answer in simplest form.
d. Write the vertex as an ordered pair (x, y). What does the vertexrepresent for this situation? Write 1-2 sentences to explain youranswer.
3. Suppose an investor builds a stock portfolio with a variety ofshares in various high tech companies. The value of the stockportfolio is modeled by the function 2x²-20x+100 , where y is thevalue of the portfolio in hundreds of dollars and x is the time inmonths.
a. Is the vertex of the function a maximum or minimum point and howcan you tell?
b. Find the x-coordinate of the vertex. Show all work leading toyour answer and write the answer in simplest form.
c. Find the y-coordinate of the vertex. Show all workleading to your answer and write the answer in simplest form.
d. Write the vertex as an ordered pair (x, y). What does the vertexrepresent for this
situation? Write 1-2 sentences to explain your answer.
