Page 801 - Algebra 1

11. Multi-Step An apple fell from a tree limb. The function t = 0.45√ x represents how (114) long it takes an object to fall from a height of x meters.
a. Graph the function. (Hint: Increment the x-axis by 1 and the y-axis by 0.1, and if a graphing calculator is not used, then use the following values for
x: 0, 4, 9, and 16.)
b. Use the graph to estimate how long it took the apple to fall if the limb was 12 meters above the ground.
12. Use the discriminant to find the number of real solutions of the equation (113) 6x2 +2x-1=0.
*13. Error Analysis Two students are using the discriminant to find the number of real (113) solutions to the equation 2x2 + 3x - 4 = 0. Which student is correct? Explain the
error.
Student A
2x2 +3x-4=0
b2 - 4ac = 32 - 4(2)(4)
= 9 - 32
= -23 As the discriminant is
negative, there are no x-intercepts.
Student B
2x2 +3x-4=0
b2 - 4ac = 32 - 4(2)(-4)
= 9 + 32
= 41
As the discriminant is positive,
there are two x-intercepts.
14. Gardening The length of a garden is 6 + x meters and the width is 10 - x meters. (113) Write an equation to model the area of the garden, and use the discriminant to
determine if there is a value for x that will allow the area of the garden to be 50 square meters.
Measurement The length of a fence is 15 - x feet and the width is 12 + x feet.
3 4 15.
(113) Can the fence enclose an area of 200 square feet? Explain.
16. Determine if the set of ordered pairs ⎧⎨ -3, _1 , -1, _1 , -2, _1 , -4, _1 ⎫⎬
(108) satisfies an exponential function. 17. Graph the system 21x + 7y ≥ -14 .
()()()() ⎩8 2 4 16⎭
(109) _1 y ≤ - x + 2 2
18. Geometry If the area of the triangle is 48 square units, what are the lengths of (110) the base and the height to the nearest whole number?
x
x+4
*19. Graph the cubic function y = 3x3. Use it to solve the equation 0 = 3x3.
(115)
20. A new 3-digit area code is being created for new telephone numbers. If the first (111) digit must be even but not 0, the second digit is 0 or 1, and the third digit can be
any number except 0, how many new area codes are possible?
786 Saxon Algebra 1