Problem 1 :
The function f is defined by f(x) = x^{2} + bx + c where b and c are constants. If the graph of f has x-intercepts at -5 and 3. Which of the following correctly gives the values of b and c ?
a) b = -5, c = 3 b) b = -3, c = 5 c) b = -2, c = - 15
d) b = 2, c = -15
Problem 2 :
y = x^{2} - 2x - 3
The parabola in the xy-plane is given by the equation above. Which of the following equivalent forms of the equation displays the coordinate of the vertex of the parabola as constants or coefficients ?
a) y = (x - 1)^{2} - 4 b) y = (x - 1)^{2} - 2
c) y = (x - 3)(x + 1) d) y + 3 = x(x + 2)
Problem 3 :
y = x^{2} + 10x + 16
The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the minimum value of y as a constant or coefficient ?
a) y = (x + 8) (x + 2) b) y - 16 = x(x + 10)
c) y = (x + 5)^{2} - 9 d) y = (x - 5)^{2} + 9
Problem 4 :
y = x^{2} - 10x + k
In the equation above, k is constant. If the equation represents a parabola in the xy-plane that is tangent to the x-axis, what is the value of k ?
Problem 5 :
A parabola is shown in the xy-plane above. Which of the following equations correctly represents the parabola by displaying the x-intercepts of the parabola as constants or coefficients ?
a) y = (x + 1.5)^{2} - 20.25 b) y = (x - 1.5)^{2} - 20.25
c) y = (x + 6)(x - 3) d) y = (x - 6)(x + 3)
Problem 6 :
The graph of the equation y = -x^{2} + 6x + 16 is a parabola with (3, 25) as shown in the xy-plane above. If one of the x-intercepts is at -2, which of the following equivalent forms of the equation shows the x-intercepts of the parabola as constant or coefficients ?
a) y = -2(x + 2)(x - 8) b) y = -(x + 2)(x - 8)
c) y = (x + 2)(x - 8) d) y = -(x - 3)^{2} + 25
Problem 7 :
In the xy-plane, the graph of a parabola has x-intercepts at -3 and 5. If the y-coordinate of the vertex of the parabola is 8, which of the following could be the equation of parabola ?
Problem 8 :
h = -6t^{2} + 36t + 12
The height of a model rocket is modeled by the equation above, where h is the height of the rocket, in meters and t is the number of seconds after launch. In which of the following equations the number of seconds it takes the rocket to reach the maximum height appear as constant or coefficients ?
a) h = -6(t +3)^{2} + 42 b) h = -6(t - 3)^{2} + 66
c) h = -6(t^{2} - 6t - 2) d) h = -6(t - 2)(t - 4) + 60
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM