A quadratic function models the graph of a parabola. The quadratic functions, y = x2 and y = x2 + 3, are modeled in the graphs of the parabolas shown below. Determine which situations best represent the scenario shown in the graph of the quadratic functions, y = x2 and y = x2 + 3. Select all that apply ( MULTIPLE CHOICE!! )

A) From x = -2 to x = 0, the average rate of change for both functions is negative.
B) For the quadratic function, y = x2, the coordinate (2, 3) is a solution to the equation of the function.
C) The quadratic function, y = x2 + 3, has an x-intercept at the origin.
D) The quadratic function, y = x2, has an x-intercept at the origin.
E) From x = -2 to x = 0, the average rate of change for both functions is positive.
D) For the quadratic function, y = x2 + 3, the coordinate (2, 7) is a solution to the equation of the function.

A, D, F

Step-by-step explanation:

A) It is seen from the graph that the average rate of change from x=-2 to x=0 is negative since the values of y are decreasing (Correct answer)

B) The coordinate (2, 3) doesn't satisfy the function y=x^2 since 2^2isn't equal to 3 (Wrong answer)

C) The x intercept is the point where the line crosses the x axis. The coordinates of the origin is (0, 0). But the function y = x^2+3 doesn't have any x-intercept (Wrong answer)

D) For the function y=x^2, when the value of x is equal to 0, the value of y is also equal to 0 so the graph of the function has an x-intercept at the origin (Correct answer)

E) The average rate of change in the given interval is negatiove. Refer to the option A (Wrong answer)

F) The coordinate (2, 7) satisfies the function y=x^2+3 (2^2+3=7) so it is a solution to the equation of the function (Correct answer)

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)