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tatiyna
2 years ago
7

Graph the function. y = 2x^2 + 4x

Mathematics
1 answer:
rodikova [14]2 years ago
3 0

Answer:

Step-by-step explanation:

The function y = 2x^2 + 4x has a parabolic graph that opens up.  

*In factored form we have y = 2x(x + 2); if we set this equal to zero and solve for x, we obtain {-2, 0}, the roots of this function.  

*The axis of symmetry is halfway between these roots:  x = -1.  The y-value of the vertex is the value of the function at x = -1:  f(-1) = 2(-1)^2 + 4(-2) = -6.  Thus, the vertex is (-1, -6).

* The y-intercept is (0, 0), since y = 0 when x = 0.

Graph the points shown and draw a smooth curve through them, remembering that this parabola opens up.

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Before a race, Evelyn ran 27 minutes to warm up. The race took her 2 hours.
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3 years ago
A train traveled from Station A to Station B at an average speed of 80 kilometers per hour and then from Station B to Station C
earnstyle [38]

Answer:

(i). Average speed = 75 km per hour

(ii). Average speed = 75 km per hour

Step-by-step explanation:

This question is incomplete; here is the complete question.

A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at an average of 60 kilometers per hour. If the train did not stop at station b, what was the average speed at which the train traveled from station A to C?

(i). The distance that the train traveled from station A to station B was 4 times the distance that train traveled from station B to station C.

(ii). The amount of time it took to the train to travel from station A to station B is 3 times the amount of time that it took the train to travel from station B to station C.

(i) Let the distance between station B and station C = x km

So the distance between Station A and station B = 4x km

Therefore, time to travel the distance x km with 80 km per hour = \frac{\text{Distance traveled}}{\text{Speed}}

= \frac{4x}{80}

Similarly time taken to travel between station B and station C with speed 60 km per hour = \frac{x}{60} km per hour

Now average speed between station A and station C = \frac{\text{Total distance between station A and station C}}{\text{time taken to travel}}

= \frac{4x+x}{\frac{4x}{80}+\frac{x}{60}}

= \frac{5x}{\frac{4x}{60} }

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(ii). Let the train took the time to cover the distance between station B and station C = t hours

Therefore, time taken by the train between station A and B = 3t

Distance between Station A and station B = Speed × time

= 80 × 3t

= 240t km

Similarly distance between station B and station C = 60 × t

= 60t

Now average speed between station A and station C = \frac{240t+60t}{(3t+t)}

= \frac{300t}{4t}

= 75 km per hour

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