A skateboard shop sells about 50 skateboards per week when each board is sold for $70 each. For each $1 decrease in price, one additional skateboard...
BY COMPLETING THE SQUARE Find the value of c that makes the expression a perfect square. Then write the expression as a square of a binomial. 1.
x 2 − 22x + c
2.
x 2 + 7x + c
2. x − x + c 2
Solve the equation by completing the square. Express yours answers in simplified radical form. 4.
x 2 + 5x + 6 = 0
5. x − 10x + 43 = 0
6.
−x 2 − 18x − 105 = 0
7. 2x − 28x + 50 = −50
8. −3x + 24x − 12 = 0
3.
x 2 − 12x + 100 = 0
2
2
2
9. Write each function in vertex form and then state its vertex. a.
y = x 2 − 2x − 8
b. y = x 2 + 5x + 4
____________
_____________
VERTEX
VERTEX
10. A skateboard shop sells about 50 skateboards per week when each board is sold for $70 each. For each $1 decrease in price, one additional skateboard per week is sold. The shop’s revenue (money from selling merchandize) represented by y, can be modeled by −(x − 70)(x + 50) = y .
a. Use intercept form of the function to find the maximum weekly revenue.
b. Rewrite the function in standard form to find the maximum weekly revenue.
c. Use the standard form from part b in order to rewrite the function in vertex form . Then use vertex form to find the maximum weekly revenue.
d. Which method do you prefer? Explain your reasoning.
11. Solve by choosing the best method. For each state the name of the method that you used. You will use each type only once. a. 2x − 1 = −51 2
