Question

Viola and Paige stand next to each other and kick soccer balls in the air. The

Answer 1

Answer:

C. Paige's soccer ball.

Step-by-step explanation:

When you graph y = 3x^2 + 6x + 3, you can see that the max of the parabola is around 6. This is lower compared to Paige's soccer ball's max height shown in the image.

Answer 2

Answer:

C. Paige's soccer ball

Step-by-step explanation:

To solve this problem, we just need to graph Viola's function to know the altitude she reached, and then compare it with Paige's altitude.

So, we know that Viola's function is $y=-3x^{2}+6x+3$, as an extra solution, we can calculate the vertex of this quadratic function, that will give us Viola's max altitude.

$V(v_{x};v_{y})\\V(\frac{-b}{2a};f(v_{x} ))$

Where b and a are from the general quadratic function: $y=ax^{2} +bx+c$.

So, in this case, a = -3; b = 6. Replacing this values, we find the vertex:

$V(\frac{-b}{2a};f(v_{x} ))$

$v_{x}= \frac{-b}{2a}=\frac{-6}{2(-3)}=1$

Then, we use the function to calculate the vertical coordinate of the vertex:

$v_{y}=f(1)=-3(1)^{2}+6(1)+3=-3+6+3=6$

Therefore, the max altitude reached by Viola is 6 meters.

Now, from the graph, we observe that Paige's max altitude is around 7.5 meters.

Therefore, Paige reached the higher height. The answer is C.