The graph below shows the distance, y, in miles, of a bird from its nest for a certain amount of time, x, in minutes:
graph titled distance vs time is shown with time in minutes along the x-axis and distance from nest in miles along the y-axis. the scale on the x-axis shows the numbers 0 to 25 at increments of 5, and the scale on the y-axis shows the numbers 1 to 8 at increments of 1. a straight line joins the ordered pairs 0, 3 and 5, 4 and 10, 5 and 15, 6 and 20, 7.
based on the graph, what is the initial value of the graph and what does it represent?
3 miles per minute; it represents the speed of the bird
0.2 mile per minute; it represents the speed of the bird
0.2 mile; it represents the original distance of the bird from its nest
3 miles; it represents the original distance of the bird from its nest
i'll go through the list of possible answers. anything marked as true i'll highlight in bold
choice a) the graph has a minimum. this is true. this is because there is a lowest point at the vertex (-1,-9)
choice b) the graph has a maximum. false. a parabola can have a min or a max but not both at the same time. choice a is true, so this contradicts choice b. the graph goes on forever upward so there is no highest point.
choice c) the graph has zeros at -4 and 2. this is true. the term "zeros" may be confusing. i like to think of them as x intercepts or roots. this is where the graph crosses or touches the x axis. they solve the equation f(x) = 0.
choice d) the vertex is located at (-1,-9). this is true. this is the lowest point of the graph. it's also where the axis of symmetry is located.
choice e) the graph has y intercepts at (-4,0) and (2,0). this is false. the parabola only crosses the y axis one time and it is at the location (0,-8) which is the y intercept. we can also say "the y intercept is -8". see choice g below. note that any function will have only y intercept. if it has more than one y intercept, then it won't be a function anymore because it fails the vertical line test.
choice f) the solution of the parabola is (-1,-9). false. a solution is another term for root or x intercept. it's where the graph crosses the x axis. in other words, it's the set of x values that make f(x) = 0 true. in this case, x = -4 and x = 2 do the trick. the vertex is not considered a solution point unless the vertex is on the x axis.
choice g) the y intercept is (0,-8). true. the graph crosses the y axis here. see choice e above.in summary, the four answers are: a, c, d, g
hello : x + 19
expression represents the other number is :
x - ( - 19) = x + 19
factor 6mn ( greatest common factor) out of the 3 terms:
6mn(4m) + 6mn(5n) + 6mn(3)
factor 6mn out of the first 2 terms:
6mn(4m + 5n +3)