This is what the directions state to do:
(A) Complete the table,(B)describe the resulting graphs by identifying the vertex point, (c) the graph’s direction, (d) and any axis intercepts gleaned from the table or graph.
Problem #1
Equation is : y = -x + 1
so These are my answers:
(A) Table : (i am going to give it in corrdinate points)
(-1 , 2 )
(0,1)
(1,0)
(B) There is no vertex & no axis of symmetry.
(C) The direction fo line is increasing on the left and decreasing on the right.
(D) Axis of intercepts are : (0,1) and (1,0)
Problem #2 (same directions as one)
Equation: y =x^2 -4x
A)Table:
(-1 , 5 )
(0,0)
(1,-3)
(2,-4)
(3,-3)
(4,0)
(5,5)
(B)Vertex (2,-4)
axis of symmetry x = 2
(c) The direction of the parabola opens upward because the coefficient has a positive x^2.
(d) Axis intercepts are : (0,0) and (4,0)
all correct.
thank you bobpursley
You're welcome! It seems like you have successfully completed the given directions for both problems. Great job! Just to explain further how you arrived at the answers:
For Problem #1:
(A) You created a table by plugging in different values of x into the equation and calculating the corresponding y-values.
(B) Since the equation y = -x + 1 is a linear equation, it represents a straight line. And since it is not a quadratic equation, it doesn't have a vertex or an axis of symmetry.
(C) By looking at the table or the graph, you determined that the line is increasing on the left (as x decreases) and decreasing on the right (as x increases).
(D) You identified the x-intercept as (1, 0) and the y-intercept as (0, 1).
For Problem #2:
(A) Again, you created a table by plugging in different values of x into the equation and calculating the corresponding y-values.
(B) This time, the equation y = x^2 - 4x represents a quadratic function, so it forms a parabola. You found the vertex of the parabola to be (2, -4) and the axis of symmetry to be x = 2.
(C) You correctly determined that the parabola opens upward since the coefficient of the x^2 term is positive.
(D) You identified the x-intercepts as (0, 0) and (4, 0).
Overall, your answers demonstrate a clear understanding of the given directions and how to analyze the graphs of the given equations. Well done!