Page 795 - Algebra 1

9. Find the value of the discriminant of the equation 2x2 - 5x - 4 = 0. (113)
*10. Error Analysis Two students are using the discriminant to find the number of (113) real solutions to the equation 5x2 - 3x = 2. Which student is correct? Explain
the error.
Student B
5x2 -3x = 2 5x2 -3x-2=0
b2 - 4ac = (-3)2 -4(5)(-2) = 9 + 40
= 49
As the discriminant is positive,
there are two x-intercepts.
Student A
5x2 -3x = 2
b2 - 4ac = (-3)2 - 4(5)(2)
= 9 - 40 = -31
As the discriminant is negative, there are no x-intercepts.
*11. Geometry The length of a rectangle is x + 12 inches and the width is x + 8 inches. (113) Is there a value for x that makes the area of the rectangle 50 square inches?
Explain your reasoning.
*12. Multi-Step The equation 288 = (3 + x)(6 - x) can be used to determine if the base (113) of a rectangular box with a length of (3 + x) inches and a width of (6 - x) inches
can have an area of 288 square inches.
a. Write the equation setting it equal to zero.
b. Use the equation to find the values of a, b, and c.
c. Find the value of the discriminant.
d. Can a box with these dimensions be made? Explain.
y = x2 + 3 13. Solve this system by graphing: .
(112) y = -2x + 3
*14. Error Analysis Two students are solving the system of equations
y=x2 +4x y = -4
by
(112) substitution. Which student is correct? Explain the error.
Student A
y = x2 + 4x y = -4 x2 +4x=-4
(x2 +4x)-4=0 x2 +4x-4=0
no solution
Student B
y = x2 + 4x y = -4 x2 +4x=-4
(x2 +4x)+4=0 x2 +4x+4=0
(x+2)(x+2)=0 So,x=-2, and the solution is (-2, -4).
*15. Physics Miguel is standing at the base of a ramp. He tosses a ball into the air. The (112) path of the ball is described by the equation y = -x2 + 7x. The equation y = x
represents the ramp. At what altitude does the ball strike the ramp? Assume that dimensions are in feet.
Measurement On what scale would the distance between the x-coordinates in the
3 4 16.
(112) y = _x 2
solution set of the system 2 be 8 centimeters? y = 4x - 6
780 Saxon Algebra 1